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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze74.0ms (1.1%)

Memory

-2.5MiB live, 77.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
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)

sample1.3s (18.9%)

Memory

38.6MiB live, 1 258.6MiB allocated

Samples

701.0ms	8 256×	0	valid
178.0ms	2 106×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 581.0ms

ival-mult: 193.0ms (33.2% of total)

ival-div: 184.0ms (31.7% of total)

ival-sqrt: 138.0ms (23.8% of total)

ival-add: 46.0ms (7.9% 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

explain99.0ms (1.4%)

Memory

-33.9MiB live, 185.6MiB 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 77 to 34 computations (55.8% saved)

Precisions

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

ival-mult: 6.0ms (36.2% of total)

ival-sqrt: 4.0ms (24.1% of total)

ival-div: 3.0ms (18.1% of total)

ival-add: 2.0ms (12.1% of total)

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

exact: 0.0ms (0% of total)

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

preprocess78.0ms (1.1%)

Memory

9.0MiB live, 47.0MiB 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 13 to 10 computations (23.1% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB 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 13 to 10 computations (23.1% saved)

simplify4.0ms (0.1%)

Memory

6.3MiB live, 6.3MiB 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

localize24.0ms (0.3%)

Memory

-1.6MiB live, 37.4MiB 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	0.19140625	(*.f64 y (sqrt.f64 z))

Samples

18.0ms

256×

valid

Compiler

Compiled 32 to 12 computations (62.5% saved)

Precisions

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

ival-mult: 3.0ms (37.3% of total)

ival-div: 2.0ms (24.8% of total)

ival-sqrt: 2.0ms (24.8% of total)

ival-add: 1.0ms (12.4% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.1%)

Memory

12.6MiB live, 12.6MiB 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))

simplify162.0ms (2.3%)

Memory

-11.4MiB live, 140.7MiB 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))

rewrite225.0ms (3.2%)

Memory

13.9MiB live, 290.2MiB 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)))) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) x)) x (.f64 (.f64 (neg.f64 z) (.f64 y y)) (.f64 (.f64 (.f64 z y) y) (.f64 (.f64 z y) y))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y)))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) (fma.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 y y) y)) (.f64 (.f64 (.f64 (.f64 y y) y) (.f64 (.f64 y y) y)) (.f64 (sqrt.f64 z) z)) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y)) (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y)) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 x x) x)))))
(.f64 (pow.f64 (/.f64 (-.f64 x (.f64 (sqrt.f64 z) y)) (.f64 (fma.f64 (.f64 z y) y (.f64 x x)) (fma.f64 (neg.f64 z) (.f64 y y) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 z y) y (*.f64 x x))))
(.f64 (pow.f64 (/.f64 (-.f64 x (.f64 (sqrt.f64 z) y)) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) x)) x (.f64 (.f64 (neg.f64 z) (.f64 y y)) (.f64 (.f64 (.f64 z y) y) (.f64 (.f64 z y) y))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 z y) y) (fma.f64 (.f64 z y) y (.f64 x x)) (.f64 (.f64 x x) (*.f64 x x)))))
(.f64 (/.f64 (fma.f64 (neg.f64 z) (.f64 y y) (.f64 x x)) (-.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y)))) (fma.f64 y (fma.f64 z y (.f64 (sqrt.f64 z) x)) (*.f64 x x)))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y) (.f64 (.f64 x x) x)) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (-.f64 (.f64 (sqrt.f64 z) y) x) (-.f64 (.f64 (sqrt.f64 z) y) x)) (.f64 (.f64 z y) y)))) (-.f64 (.f64 x x) (.f64 y (-.f64 (.f64 z y) (*.f64 (sqrt.f64 z) x)))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y) (.f64 (.f64 x x) x)) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) x)) x (.f64 (.f64 (.f64 (-.f64 (.f64 (sqrt.f64 z) y) x) (-.f64 (.f64 (sqrt.f64 z) y) x)) (.f64 (.f64 z y) y)) (.f64 y (-.f64 (.f64 z y) (.f64 (sqrt.f64 z) x)))))) (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)) (.f64 (.f64 x x) (.f64 x x))))
(.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 (fma.f64 (.f64 z y) y (.f64 x x)) (fma.f64 (neg.f64 z) (.f64 y y) (.f64 x x))) (-.f64 x (.f64 (sqrt.f64 z) y))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 z y) y (*.f64 x x))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) x)) x (.f64 (.f64 (neg.f64 z) (.f64 y y)) (.f64 (.f64 (.f64 z y) y) (.f64 (.f64 z y) y)))) (-.f64 x (.f64 (sqrt.f64 z) y))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 z y) y) (fma.f64 (.f64 z y) y (.f64 x x)) (.f64 (.f64 x x) (*.f64 x x)))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) x)) x (.f64 (.f64 (neg.f64 z) (.f64 y y)) (.f64 (.f64 (.f64 z y) y) (.f64 (.f64 z y) y)))) (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y))))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y)))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 y y) y)) (.f64 (.f64 (.f64 (.f64 y y) y) (.f64 (.f64 y y) y)) (.f64 (sqrt.f64 z) z)) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x))) (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y)) (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y)) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 x x) x)))))
(.f64 (.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y) (.f64 (.f64 x x) x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y))))))
(.f64 (-.f64 (.f64 (.f64 x (/.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) (.f64 x (/.f64 x (-.f64 x (.f64 (sqrt.f64 z) y))))) (.f64 (.f64 (.f64 z y) (/.f64 y (-.f64 x (.f64 (sqrt.f64 z) y)))) (.f64 (.f64 z y) (/.f64 y (-.f64 x (.f64 (sqrt.f64 z) y)))))) (/.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 (.f64 (.f64 x (/.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) (.f64 x (/.f64 x (-.f64 x (.f64 (sqrt.f64 z) y))))) (.f64 x (/.f64 x (-.f64 x (.f64 (sqrt.f64 z) y))))) (.f64 (.f64 (.f64 (.f64 z y) (/.f64 y (-.f64 x (.f64 (sqrt.f64 z) y)))) (.f64 (.f64 z y) (/.f64 y (-.f64 x (.f64 (sqrt.f64 z) y))))) (.f64 (.f64 z y) (/.f64 y (-.f64 x (.f64 (sqrt.f64 z) y)))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (/.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) (.f64 x (/.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) (fma.f64 (.f64 (.f64 z y) (/.f64 y (-.f64 x (.f64 (sqrt.f64 z) y)))) (.f64 (.f64 z y) (/.f64 y (-.f64 x (.f64 (sqrt.f64 z) y)))) (.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)))) (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 (sqrt.f64 z) y))))
(.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y) (.f64 (.f64 x x) x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))))))
(.f64 (.f64 (.f64 (fma.f64 (.f64 z y) y (.f64 x x)) (fma.f64 (neg.f64 z) (.f64 y y) (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 z y) y (.f64 x x)) (-.f64 x (*.f64 (sqrt.f64 z) y)))))
(.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) x)) x (.f64 (.f64 (neg.f64 z) (.f64 y y)) (.f64 (.f64 (.f64 z y) y) (.f64 (.f64 z y) y)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 (.f64 z y) y) (fma.f64 (.f64 z y) y (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) (-.f64 x (*.f64 (sqrt.f64 z) y)))))
(.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) x)) x (.f64 (.f64 (neg.f64 z) (.f64 y y)) (.f64 (.f64 (.f64 z y) y) (.f64 (.f64 z y) y)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y))) (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))))))
(.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 y y) y)) (.f64 (.f64 (.f64 (.f64 y y) y) (.f64 (.f64 y y) y)) (.f64 (sqrt.f64 z) z)) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y)) (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y)) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (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) (.f64 (-.f64 x (.f64 (sqrt.f64 z) y)) (-.f64 x (*.f64 (sqrt.f64 z) y)))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 z) y x)))))
(.f64 (.f64 (fma.f64 (.f64 z y) y (.f64 x x)) (fma.f64 (neg.f64 z) (.f64 y y) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x (.f64 (sqrt.f64 z) y)) (fma.f64 (.f64 z y) y (.f64 x x)))))
(.f64 (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) x)) x (.f64 (.f64 (neg.f64 z) (.f64 y y)) (.f64 (.f64 (.f64 z y) y) (.f64 (.f64 z y) y)))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x (.f64 (sqrt.f64 z) y)) (fma.f64 (.f64 (.f64 z y) y) (fma.f64 (.f64 z y) y (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) x)) x (.f64 (.f64 (neg.f64 z) (.f64 y y)) (.f64 (.f64 (.f64 z y) y) (.f64 (.f64 z y) y)))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) (-.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (*.f64 y y))))))
(.f64 (fma.f64 (.f64 z y) y (.f64 (neg.f64 x) x)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (sqrt.f64 z) y) x)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 (sqrt.f64 z) y))) (fma.f64 (neg.f64 z) (.f64 y y) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y))))) (fma.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y) (.f64 (*.f64 x x) x)))
(.f64 (fma.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 y y) y)) (.f64 (.f64 (.f64 (.f64 y y) y) (.f64 (.f64 y y) y)) (.f64 (sqrt.f64 z) z)) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y)) (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y)) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))))))
(.f64 (neg.f64 (fma.f64 (neg.f64 z) (.f64 y y) (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x (.f64 (sqrt.f64 z) y)))))
(.f64 (neg.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (.f64 y y) (.f64 (.f64 x x) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y)))))))
(.f64 (fma.f64 (neg.f64 z) (.f64 y y) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 (sqrt.f64 z) y))))
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(fma.f64 (sqrt.f64 z) (.f64 y #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 y (.f64 (sqrt.f64 z) #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 z) y) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (.f64 (.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 z y) y)) (-.f64 (.f64 (.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (.f64 (.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (-.f64 x (.f64 (sqrt.f64 z) y)))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 z y) y)) (.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 (sqrt.f64 z) y)))))
(+.f64 (.f64 (.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)))
(*.f64 (exp.f64 (log.f64 y)) (sqrt.f64 z))
(.f64 (pow.f64 (.f64 y (pow.f64 z #s(literal 1/4 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (.f64 (pow.f64 z #s(literal 1/4 binary64)) y) #s(literal 1 binary64)))
(*.f64 (pow.f64 y #s(literal 1 binary64)) (sqrt.f64 z))
(.f64 (.f64 y (pow.f64 z #s(literal 1/4 binary64))) (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 (sqrt.f64 z) (exp.f64 (log.f64 y)))
(*.f64 (sqrt.f64 z) (pow.f64 y #s(literal 1 binary64)))
(*.f64 (sqrt.f64 z) y)
(*.f64 y (sqrt.f64 z))
(pow.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1 binary64))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 z) y)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 z) y)))
(*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))))
(*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))
(*.f64 (pow.f64 (pow.f64 z #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 z #s(literal 3/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 z #s(literal 1/4 binary64)) (pow.f64 z #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z))
(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 (sqrt.f64 z) #s(literal 1 binary64))
(pow.f64 z #s(literal 1/2 binary64))
(sqrt.f64 z)
(fabs.f64 (sqrt.f64 z))
(exp.f64 (fma.f64 (log.f64 z) #s(literal 1/4 binary64) (*.f64 (log.f64 z) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 z) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 z z)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 z #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 z) #s(literal 1/2 binary64)))

eval52.0ms (0.7%)

Memory: -7.2MiB live, 117.1MiB allocated
Compiler: Compiled 11 782 to 920 computations (92.2% saved)

prune58.0ms (0.8%)

Memory

24.5MiB live, 139.8MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	368	9	377
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	369	9	378

Accuracy

100.0%

Counts

378 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 z) y x)))
▶	99.8%	(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
	86.9%	(.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 (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)))))
▶	66.2%	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (pow.f64 (*.f64 z z) #s(literal 1/4 binary64)))))
▶	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))))))
▶	93.2%	#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)))
	54.0%	#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 z) y)))
▶	47.8%	#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 268 to 180 computations (32.8% saved)

simplify10.0ms (0.1%)

Memory

-24.2MiB live, 20.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64)))
cost-diff	0	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (pow.f64 (*.f64 z z) #s(literal 1/4 binary64)))))
cost-diff	128	(+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64))))
cost-diff	704	(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
cost-diff	0	(.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))))))
cost-diff	128	(+.f64 x (.f64 y (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))
cost-diff	704	(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
cost-diff	2240	(*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))
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	(.f64 (fma.f64 (.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))
cost-diff	0	#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)))
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	(fma.f64 (sqrt.f64 z) y x)
cost-diff	0	(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))

Rules

196×	`lower-*.f32`
176×	`lower-*.f64`
96×	`lower-fma.f32`
92×	`lower-fma.f64`
84×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	183
0	59	159
1	97	159
2	136	159
3	186	159
4	219	159
0	219	157

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize119.0ms (1.7%)

Memory

2.8MiB live, 159.8MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 z z)
accuracy	0.00390625	(+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64))))
accuracy	0.19140625	(.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64)))
accuracy	31.627353425591718	(pow.f64 (*.f64 z z) #s(literal 1/4 binary64))
accuracy	0.00390625	(+.f64 x (.f64 y (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))
accuracy	0.1171875	(sqrt.f64 (sqrt.f64 z))
accuracy	0.19140625	(.f64 y (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))
accuracy	0.4990425293053261	(*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))
accuracy	0	(*.f64 z y)
accuracy	0	#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)))
accuracy	0.1015625	(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
accuracy	4.348948222487728	(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	33.392936266657806	#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
accuracy	0	(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
accuracy	0	(sqrt.f64 z)
accuracy	0.10546875	(fma.f64 (sqrt.f64 z) y x)

Samples

98.0ms

256×

valid

Compiler

Compiled 185 to 34 computations (81.6% saved)

Precisions

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

ival-mult: 20.0ms (49% of total)

ival-pow: 7.0ms (17.1% of total)

ival-add: 5.0ms (12.2% of total)

ival-sqrt: 5.0ms (12.2% of total)

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

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

exact: 0.0ms (0% of total)

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

series252.0ms (3.6%)

Memory

17.6MiB live, 453.8MiB allocated

Counts

21 → 516

Calls

Call 1

Inputs
#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 (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 #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))) (patch #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))) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 (.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) #<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 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))) (patch (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))) #<representation binary64>) () ())
#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 (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))) (patch (+.f64 x (.f64 y (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))) #<representation binary64>) () ())
#s(alt (.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)))))) (patch (.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)))))) #<representation binary64>) () ())
#s(alt (+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64)))) (patch (+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64))))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64))) (patch (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 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 y (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))) (patch (.f64 y (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (sqrt.f64 z)) (patch (sqrt.f64 (sqrt.f64 z)) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 z z) #s(literal 1/4 binary64)) (patch (pow.f64 (.f64 z z) #s(literal 1/4 binary64)) #<representation binary64>) () ())
#s(alt (.f64 z z) (patch (.f64 z z) #<representation binary64>) () ())

Outputs
#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>) () ())) ())
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#s(alt x (taylor -inf x) (#s(alt (+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64)))) (patch (+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64)))) (patch (+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64)))) (patch (+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64)))) (patch (+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64)))) #<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 (pow.f64 (.f64 z z) #s(literal 1/4 binary64))))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64))))) #<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 (pow.f64 (.f64 z z) #s(literal 1/4 binary64))))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64))))) #<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 (pow.f64 (.f64 z z) #s(literal 1/4 binary64))))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64))))) #<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 (pow.f64 (.f64 z z) #s(literal 1/4 binary64))))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (pow.f64 (.f64 z z) #s(literal 1/4 binary64))))) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
78.0ms	z	@	0	((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (sqrt (/ 1 z))) x) 1/2) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (* (sqrt (sqrt z)) (sqrt (sqrt z))) (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z))))) (* (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))))) (+ x (* y (pow (* z z) 1/4))) (* (/ 1 2) (+ x (* y (pow (* z z) 1/4)))) (* y (pow (* z z) 1/4)) (sqrt (/ 1 z)) (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))) (sqrt (sqrt z)) (pow (* z z) 1/4) (* z z))
46.0ms	z	@	inf	((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (sqrt (/ 1 z))) x) 1/2) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (* (sqrt (sqrt z)) (sqrt (sqrt z))) (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z))))) (* (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))))) (+ x (* y (pow (* z z) 1/4))) (* (/ 1 2) (+ x (* y (pow (* z z) 1/4)))) (* y (pow (* z z) 1/4)) (sqrt (/ 1 z)) (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))) (sqrt (sqrt z)) (pow (* z z) 1/4) (* z z))
24.0ms	y	@	-inf	((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (sqrt (/ 1 z))) x) 1/2) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (* (sqrt (sqrt z)) (sqrt (sqrt z))) (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z))))) (* (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))))) (+ x (* y (pow (* z z) 1/4))) (* (/ 1 2) (+ x (* y (pow (* z z) 1/4)))) (* y (pow (* z z) 1/4)) (sqrt (/ 1 z)) (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))) (sqrt (sqrt z)) (pow (* z z) 1/4) (* z z))
24.0ms	z	@	-inf	((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (sqrt (/ 1 z))) x) 1/2) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (* (sqrt (sqrt z)) (sqrt (sqrt z))) (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z))))) (* (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))))) (+ x (* y (pow (* z z) 1/4))) (* (/ 1 2) (+ x (* y (pow (* z z) 1/4)))) (* y (pow (* z z) 1/4)) (sqrt (/ 1 z)) (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))) (sqrt (sqrt z)) (pow (* z z) 1/4) (* z z))
14.0ms	y	@	0	((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (sqrt (/ 1 z))) x) 1/2) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (* (sqrt (sqrt z)) (sqrt (sqrt z))) (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z))))) (* (/ 1 2) (+ x (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))))) (+ x (* y (pow (* z z) 1/4))) (* (/ 1 2) (+ x (* y (pow (* z z) 1/4)))) (* y (pow (* z z) 1/4)) (sqrt (/ 1 z)) (* y (* (sqrt (sqrt z)) (sqrt (sqrt z)))) (sqrt (sqrt z)) (pow (* z z) 1/4) (* z z))

simplify154.0ms (2.2%)

Memory

-1.6MiB live, 202.3MiB allocated

Algorithm

1×	egg-herbie

Rules

7 230×	`lower-fma.f64`
7 230×	`lower-fma.f32`
3 558×	`lower-*.f64`
3 558×	`lower-*.f32`
1 990×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	108	3358
1	357	3307
2	1360	3291
3	2543	3156
4	5635	3156
5	7787	3156
0	8128	2888

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 504

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

rewrite232.0ms (3.3%)

Memory

4.8MiB live, 234.2MiB allocated

Rules

8 428×	`lower-fma.f32`
8 424×	`lower-fma.f64`
4 074×	`lower-*.f32`
4 060×	`lower-*.f64`
1 708×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	155
0	59	115
1	184	107
2	919	104
3	7634	104
0	8155	104

Stop Event

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

Counts

21 → 1 209

Calls

Call 1

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

Outputs
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(/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 z)) (.f64 (sqrt.f64 (neg.f64 z)) #s(literal -1 binary64)))
(/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (sqrt.f64 (neg.f64 z)) (/.f64 #s(literal 1 binary64) z)))
(/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) (.f64 (sqrt.f64 (neg.f64 z)) #s(literal 1 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) z) (sqrt.f64 (neg.f64 z)))
(/.f64 (.f64 (neg.f64 z) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 z)))) (.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 z))))
(/.f64 (.f64 (neg.f64 z) (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal -1 binary64) (sqrt.f64 (neg.f64 z))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 (/.f64 #s(literal 1 binary64) z) (sqrt.f64 (neg.f64 z))))
(/.f64 (.f64 z (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 z)))) (.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 z))))
(/.f64 (*.f64 z (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 z)))
(/.f64 (.f64 z (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 z))))
(/.f64 (*.f64 z (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (neg.f64 z)))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 z)) (.f64 (sqrt.f64 z) #s(literal -1 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 z))) (*.f64 (/.f64 #s(literal 1 binary64) z) (sqrt.f64 (sqrt.f64 z))))
(/.f64 (neg.f64 (sqrt.f64 z)) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (neg.f64 z)) (sqrt.f64 #s(literal -1 binary64)))
(/.f64 (neg.f64 z) (*.f64 (neg.f64 (sqrt.f64 z)) #s(literal 1 binary64)))
(/.f64 (neg.f64 z) (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 z))))
(/.f64 (neg.f64 z) (neg.f64 (sqrt.f64 z)))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (sqrt.f64 z)) (/.f64 #s(literal 1 binary64) z)))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) z) (neg.f64 (sqrt.f64 z))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) (/.f64 #s(literal 1 binary64) z))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 z) (/.f64 #s(literal 1 binary64) z)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) z) (sqrt.f64 z)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))
(/.f64 (sqrt.f64 z) #s(literal 1 binary64))
(/.f64 z (*.f64 (neg.f64 (sqrt.f64 z)) #s(literal -1 binary64)))
(/.f64 z (*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 z))))
(/.f64 z (sqrt.f64 z))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) z) (.f64 z z)))
(sqrt.f64 (.f64 (.f64 z z) (/.f64 #s(literal 1 binary64) z)))
(sqrt.f64 z)
(fabs.f64 (neg.f64 (sqrt.f64 z)))
(fabs.f64 (sqrt.f64 z))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 (.f64 z z) z) z)) #s(literal 1/8 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 z) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 z) #s(literal 1/2 binary64)))
(.f64 (.f64 z (sqrt.f64 (*.f64 (sqrt.f64 z) z))) (sqrt.f64 (sqrt.f64 z)))
(.f64 (.f64 z (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (*.f64 (sqrt.f64 z) z)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (sqrt.f64 z) z)) #s(literal 2 binary64)) (sqrt.f64 z))
(.f64 (sqrt.f64 (.f64 (sqrt.f64 z) z)) (*.f64 (sqrt.f64 (sqrt.f64 z)) z))
(.f64 (.f64 (sqrt.f64 z) z) (sqrt.f64 z))
(.f64 (.f64 z z) #s(literal 1 binary64))
(.f64 (sqrt.f64 (sqrt.f64 z)) (.f64 (sqrt.f64 (*.f64 (sqrt.f64 z) z)) z))
(.f64 (sqrt.f64 z) (pow.f64 (sqrt.f64 (.f64 (sqrt.f64 z) z)) #s(literal 2 binary64)))
(.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) z))
(*.f64 z z)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 z))
(pow.f64 (.f64 (.f64 (*.f64 z z) z) z) #s(literal 1/2 binary64))
(pow.f64 (*.f64 z z) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 z)) #s(literal 8 binary64))
(pow.f64 (sqrt.f64 z) #s(literal 4 binary64))
(pow.f64 z #s(literal 2 binary64))
(/.f64 (*.f64 (neg.f64 z) (neg.f64 z)) #s(literal 1 binary64))
(/.f64 (*.f64 (neg.f64 z) z) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 z)) (/.f64 #s(literal -1 binary64) z))
(/.f64 (*.f64 z (neg.f64 z)) #s(literal -1 binary64))
(/.f64 (neg.f64 z) (/.f64 #s(literal -1 binary64) z))
(/.f64 (*.f64 z z) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) z) (/.f64 #s(literal 1 binary64) z)))
(/.f64 z (/.f64 #s(literal 1 binary64) z))
(sqrt.f64 (.f64 (.f64 (*.f64 z z) z) z))
(exp.f64 (*.f64 (log.f64 z) #s(literal 2 binary64)))

eval325.0ms (4.6%)

Memory: 10.9MiB live, 395.0MiB allocated
Compiler: Compiled 41 208 to 2 538 computations (93.8% saved)

prune642.0ms (9.2%)

Memory

4.3MiB live, 240.4MiB allocated

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	1 905	5	1 910
Fresh	3	1	4
Picked	3	2	5
Done	0	0	0
Total	1 911	8	1 919

Accuracy

100.0%

Counts

1 919 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 z) y x)))
▶	99.7%	(*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64))
▶	91.1%	(*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64))
▶	93.2%	(.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) (.f64 y z) x) #s(literal 1/2 binary64))
	74.4%	(.f64 (fma.f64 (.f64 (/.f64 y (sqrt.f64 z)) (sqrt.f64 (*.f64 (sqrt.f64 z) z))) (sqrt.f64 (sqrt.f64 z)) x) #s(literal 1/2 binary64))
✓	99.8%	(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
▶	54.0%	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
✓	47.8%	#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 177 to 120 computations (32.2% saved)

simplify14.0ms (0.2%)

Memory

9.6MiB live, 9.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

208×	`lower-*.f32`
200×	`lower-*.f64`
114×	`associate-r`
84×	`associate-l`
80×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	145
0	44	139
1	67	139
2	103	139
3	177	139
4	276	139
5	276	139
6	327	139
7	327	139
8	329	139
9	334	139
10	334	139
0	334	139

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize80.0ms (1.1%)

Memory

-8.8MiB live, 84.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 z)
accuracy	0.10546875	(fma.f64 (sqrt.f64 z) y x)
accuracy	0.21875	(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 z) y x)))
accuracy	0.4763012426392841	(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 z) y x))
accuracy	0	(*.f64 y z)
accuracy	0	(sqrt.f64 z)
accuracy	0.296875	(/.f64 #s(literal 1 binary64) (sqrt.f64 z))
accuracy	4.348948222487728	(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) (*.f64 y z) x)
accuracy	0	(*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64))
accuracy	0	(sqrt.f64 z)
accuracy	0.21875	(/.f64 y (sqrt.f64 z))
accuracy	5.662903710954806	(fma.f64 (/.f64 y (sqrt.f64 z)) z 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	0.19140625	(*.f64 (sqrt.f64 z) y)
accuracy	29.361762891847746	#s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y))
accuracy	0	(*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #s(literal 1/2 binary64))
accuracy	0	(sqrt.f64 z)
accuracy	0.10546875	(fma.f64 (/.f64 z (sqrt.f64 z)) y x)
accuracy	0.54296875	(/.f64 z (sqrt.f64 z))

Samples

51.0ms

256×

valid

Compiler

Compiled 148 to 26 computations (82.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-mult: 19.0ms (56.3% of total)

ival-div: 7.0ms (20.7% of total)

ival-add: 4.0ms (11.8% of total)

ival-sqrt: 2.0ms (5.9% of total)

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

exact: 0.0ms (0% of total)

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

series49.0ms (0.7%)

Memory

-20.8MiB live, 54.5MiB allocated

Counts

17 → 504

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
20.0ms	z	@	inf	((* (+ (* (/ z (sqrt z)) y) x) 1/2) (+ (* (/ z (sqrt z)) y) x) (/ z (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (+ (* (/ 1 (sqrt z)) (* y z)) x) (* (+ (* (/ 1 (sqrt z)) (* y z)) x) 1/2) (/ 1 (sqrt z)) (/ 1/2 (/ 1 (+ (* (sqrt z) y) x))) (/ 1 (+ (* (sqrt z) y) x)) (+ (* (sqrt z) y) x) (* y z))
4.0ms	z	@	-inf	((* (+ (* (/ z (sqrt z)) y) x) 1/2) (+ (* (/ z (sqrt z)) y) x) (/ z (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (+ (* (/ 1 (sqrt z)) (* y z)) x) (* (+ (* (/ 1 (sqrt z)) (* y z)) x) 1/2) (/ 1 (sqrt z)) (/ 1/2 (/ 1 (+ (* (sqrt z) y) x))) (/ 1 (+ (* (sqrt z) y) x)) (+ (* (sqrt z) y) x) (* y z))
2.0ms	y	@	0	((* (+ (* (/ z (sqrt z)) y) x) 1/2) (+ (* (/ z (sqrt z)) y) x) (/ z (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (+ (* (/ 1 (sqrt z)) (* y z)) x) (* (+ (* (/ 1 (sqrt z)) (* y z)) x) 1/2) (/ 1 (sqrt z)) (/ 1/2 (/ 1 (+ (* (sqrt z) y) x))) (/ 1 (+ (* (sqrt z) y) x)) (+ (* (sqrt z) y) x) (* y z))
2.0ms	y	@	-inf	((* (+ (* (/ z (sqrt z)) y) x) 1/2) (+ (* (/ z (sqrt z)) y) x) (/ z (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (+ (* (/ 1 (sqrt z)) (* y z)) x) (* (+ (* (/ 1 (sqrt z)) (* y z)) x) 1/2) (/ 1 (sqrt z)) (/ 1/2 (/ 1 (+ (* (sqrt z) y) x))) (/ 1 (+ (* (sqrt z) y) x)) (+ (* (sqrt z) y) x) (* y z))
2.0ms	z	@	0	((* (+ (* (/ z (sqrt z)) y) x) 1/2) (+ (* (/ z (sqrt z)) y) x) (/ z (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (+ (* (/ 1 (sqrt z)) (* y z)) x) (* (+ (* (/ 1 (sqrt z)) (* y z)) x) 1/2) (/ 1 (sqrt z)) (/ 1/2 (/ 1 (+ (* (sqrt z) y) x))) (/ 1 (+ (* (sqrt z) y) x)) (+ (* (sqrt z) y) x) (* y z))

simplify164.0ms (2.3%)

Memory

12.6MiB live, 205.4MiB allocated

Algorithm

1×	egg-herbie

Rules

7 288×	`lower-fma.f64`
7 288×	`lower-fma.f32`
4 804×	`lower-*.f64`
4 804×	`lower-*.f32`
3 662×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	271	4149
1	879	4066
2	2856	4026
3	7874	4011
0	8397	3780

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 489

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

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

rewrite215.0ms (3.1%)

Memory

17.0MiB live, 330.5MiB allocated

Rules

6 382×	`lower-fma.f32`
6 376×	`lower-fma.f64`
3 298×	`lower-*.f32`
3 290×	`lower-*.f64`
1 652×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	116
0	44	116
1	146	115
2	793	95
3	6643	95
0	8058	95

Stop Event

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

Counts

17 → 2 061

Calls

Call 1

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

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

eval595.0ms (8.5%)

Memory: -148.1MiB live, 693.7MiB allocated
Compiler: Compiled 46 332 to 3 117 computations (93.3% saved)

prune363.0ms (5.2%)

Memory

-14.8MiB live, 379.7MiB allocated

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	2 758	4	2 762
Fresh	1	0	1
Picked	3	2	5
Done	0	2	2
Total	2 762	8	2 770

Accuracy

100.0%

Counts

2 770 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(*.f64 (fma.f64 (/.f64 z (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))
▶	48.6%	(.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64))
▶	53.9%	(.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64))
▶	53.9%	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y)) #s(literal 1/2 binary64))
▶	46.8%	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64))
✓	54.0%	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
✓	47.8%	#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 87 to 60 computations (31% saved)

simplify8.0ms (0.1%)

Memory

9.8MiB live, 9.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

72×	`lower-*.f32`
62×	`lower-*.f64`
30×	`lower-/.f32`
24×	`*-commutative`
22×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	172
0	38	172
1	52	166
2	54	166
3	65	166
4	73	166
5	89	166
6	99	166
7	107	166
8	109	166
0	109	158

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

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

localize50.0ms (0.7%)

Memory

-4.1MiB live, 73.1MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y z)
accuracy	0	(sqrt.f64 z)
accuracy	6.910071321810065	(/.f64 (*.f64 y z) (sqrt.f64 z))
accuracy	29.361762891847746	#s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z)))
accuracy	0	(sqrt.f64 z)
accuracy	0.23828125	(/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))
accuracy	0.296875	(/.f64 #s(literal 1 binary64) (sqrt.f64 z))
accuracy	29.361762891847746	#s(approx (+ (* (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z))))
accuracy	0	(sqrt.f64 z)
accuracy	0.19140625	(*.f64 (/.f64 z (sqrt.f64 z)) y)
accuracy	0.54296875	(/.f64 z (sqrt.f64 z))
accuracy	29.361762891847746	#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y))
accuracy	0	(sqrt.f64 z)
accuracy	0.21875	(/.f64 y (sqrt.f64 z))
accuracy	9.002320142255737	(*.f64 (/.f64 y (sqrt.f64 z)) z)
accuracy	29.361762891847746	#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z))

Samples

37.0ms

256×

valid

Compiler

Compiled 118 to 19 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-mult: 13.0ms (55.2% of total)

ival-div: 7.0ms (29.7% of total)

ival-sqrt: 2.0ms (8.5% of total)

ival-add: 1.0ms (4.2% of total)

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

exact: 0.0ms (0% of total)

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

series53.0ms (0.8%)

Memory

-4.2MiB live, 33.9MiB 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 z (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (sqrt z) y) x) (.f64 (/.f64 z (sqrt.f64 z)) y)) (patch #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 z (sqrt.f64 z)) y) (patch (.f64 (/.f64 z (sqrt.f64 z)) y) #<representation binary64>) () ())
#s(alt (/.f64 z (sqrt.f64 z)) (patch (/.f64 z (sqrt.f64 z)) #<representation binary64>) () ())
#s(alt (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z))) (patch (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) (patch (/.f64 #s(literal 1 binary64) (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 (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 z (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 z (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 (/.f64 z (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 z (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 (/.f64 z (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 z (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 (/.f64 z (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 z (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 (/.f64 z (sqrt.f64 z)) y)) (patch #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (.f64 (/.f64 z (sqrt.f64 z)) y)) (patch #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (.f64 (/.f64 z (sqrt.f64 z)) y)) (patch #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (.f64 (/.f64 z (sqrt.f64 z)) y)) (patch #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y)) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (.f64 (/.f64 z (sqrt.f64 z)) y) (patch (.f64 (/.f64 z (sqrt.f64 z)) y) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (.f64 (/.f64 z (sqrt.f64 z)) y) (patch (.f64 (/.f64 z (sqrt.f64 z)) y) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (.f64 (/.f64 z (sqrt.f64 z)) y) (patch (.f64 (/.f64 z (sqrt.f64 z)) y) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (.f64 (/.f64 z (sqrt.f64 z)) y) (patch (.f64 (/.f64 z (sqrt.f64 z)) y) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (/.f64 z (sqrt.f64 z)) (patch (/.f64 z (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (/.f64 z (sqrt.f64 z)) (patch (/.f64 z (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (/.f64 z (sqrt.f64 z)) (patch (/.f64 z (sqrt.f64 z)) #<representation binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (/.f64 z (sqrt.f64 z)) (patch (/.f64 z (sqrt.f64 z)) #<representation binary64>) () ())) ())
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#s(alt (* 1/2 x) (taylor inf x) (#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 (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) (taylor inf x) (#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 (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) (taylor inf x) (#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 (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) (taylor inf x) (#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 (taylor inf x) (#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 (+ 1 (* (/ y x) (sqrt z)))) (taylor inf x) (#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 (+ 1 (* (/ y x) (sqrt z)))) (taylor inf x) (#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 (+ 1 (* (/ y x) (sqrt z)))) (taylor inf x) (#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 (* 1/2 x) (taylor -inf x) (#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 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#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 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#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 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#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 (taylor -inf x) (#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 (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#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 (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#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 (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#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 (* 1/2 x) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (sqrt z) y) x) (.f64 (/.f64 z (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y)) #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(approx (+ ( (sqrt z) y) x) (.f64 (/.f64 z (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y)) #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(approx (+ ( (sqrt z) y) x) (.f64 (/.f64 z (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y)) #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(approx (+ ( (sqrt z) y) x) (.f64 (/.f64 z (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (.f64 (/.f64 z (sqrt.f64 z)) y)) (patch #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (.f64 (/.f64 z (sqrt.f64 z)) y)) (patch #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (.f64 (/.f64 z (sqrt.f64 z)) y)) (patch #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (.f64 (/.f64 z (sqrt.f64 z)) y)) (patch #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #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(approx (+ ( (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #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(approx (+ ( (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #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(approx (+ ( (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#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 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#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 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#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 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#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 (taylor -inf x) (#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 (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#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 (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#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 (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#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>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	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) (* (/ z (sqrt z)) y) (/ z (sqrt z)) (/ y (/ 1 (sqrt z))) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ 1 (sqrt z)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* y z) (sqrt z)) (* y z) (sqrt z))
1.0ms	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) (* (/ z (sqrt z)) y) (/ z (sqrt z)) (/ y (/ 1 (sqrt z))) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ 1 (sqrt z)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* y z) (sqrt z)) (* y z) (sqrt z))
1.0ms	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) (* (/ z (sqrt z)) y) (/ z (sqrt z)) (/ y (/ 1 (sqrt z))) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ 1 (sqrt z)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* y z) (sqrt z)) (* y z) (sqrt z))
1.0ms	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) (* (/ z (sqrt z)) y) (/ z (sqrt z)) (/ y (/ 1 (sqrt z))) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ 1 (sqrt z)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* y z) (sqrt z)) (* y z) (sqrt z))
1.0ms	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) (* (/ z (sqrt z)) y) (/ z (sqrt z)) (/ y (/ 1 (sqrt z))) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ 1 (sqrt z)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* y z) (sqrt z)) (* y z) (sqrt z))

simplify141.0ms (2%)

Memory

13.7MiB live, 139.8MiB 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	76	2800
1	253	2800
2	795	2800
3	2296	2704
4	5074	2704
5	7562	2704
0	8152	2480

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 456

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

rewrite172.0ms (2.5%)

Memory

-13.8MiB live, 176.5MiB allocated

Rules

3 896×	`lower-fma.f64`
3 896×	`lower-fma.f32`
3 746×	`lower-/.f32`
3 736×	`lower-/.f64`
3 080×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	153
0	38	155
1	95	154
2	399	126
3	3198	126
0	8356	118

Stop Event

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

Counts

17 → 724

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

eval164.0ms (2.3%)

Memory: 27.9MiB live, 332.7MiB allocated
Compiler: Compiled 17 472 to 1 985 computations (88.6% saved)

prune182.0ms (2.6%)

Memory

-32.0MiB live, 257.5MiB allocated

Pruning

9 alts after pruning (1 fresh and 8 done)

	Pruned	Kept	Total
New	1 440	1	1 441
Fresh	0	0	0
Picked	0	4	4
Done	0	4	4
Total	1 440	9	1 449

Accuracy

100.0%

Counts

1 449 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(*.f64 (fma.f64 (/.f64 z (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))
✓	48.6%	(.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64))
✓	53.9%	(.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64))
✓	53.9%	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y)) #s(literal 1/2 binary64))
✓	46.8%	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64))
	46.8%	(.f64 #s(approx (+ ( (sqrt z) y) x) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) y) z)) #s(literal 1/2 binary64))
✓	54.0%	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
✓	47.8%	#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 321 to 143 computations (55.5% saved)

regimes64.0ms (0.9%)

Memory

35.4MiB live, 74.8MiB allocated

Counts

20 → 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(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 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64))
(*.f64 (fma.f64 (/.f64 z (sqrt.f64 z)) y x) #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 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 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 y (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64))
(.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 z)) (.f64 y z) x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 z) y x)))
(.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 (fma.f64 (.f64 (/.f64 y (sqrt.f64 z)) (sqrt.f64 (*.f64 (sqrt.f64 z) z))) (sqrt.f64 (sqrt.f64 z)) x) #s(literal 1/2 binary64))
(.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)))))))
(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (pow.f64 (*.f64 z z) #s(literal 1/4 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)))))

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

Calls

7 calls:

28.0ms	z
6.0ms	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z))))
6.0ms	(sqrt.f64 z)
6.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
6.0ms	y

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 46 to 34 computations (26.1% saved)

regimes16.0ms (0.2%)

Memory

-3.7MiB live, 33.8MiB 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) 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))

Calls

7 calls:

5.0ms	(*.f64 y (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
2.0ms	(sqrt.f64 z)

Results

Accuracy	Segments	Branch
79.1%	3	`x`
77.3%	3	`y`
62.1%	3	`z`
67.7%	7	`(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z))))`
67.7%	7	`(+.f64 x (*.f64 y (sqrt.f64 z)))`
78.4%	3	`(*.f64 y (sqrt.f64 z))`
62.1%	3	`(sqrt.f64 z)`

Compiler

Compiled 46 to 34 computations (26.1% saved)

regimes12.0ms (0.2%)

Memory

-13.5MiB live, 24.5MiB 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:

4.0ms	(sqrt.f64 z)
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	z
1.0ms	y

Results

Accuracy	Segments	Branch
47.8%	1	`(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z))))`
47.8%	1	`(+.f64 x (*.f64 y (sqrt.f64 z)))`
47.8%	1	`z`
47.8%	1	`(sqrt.f64 z)`
47.8%	1	`y`
47.8%	1	`(*.f64 y (sqrt.f64 z))`
47.8%	1	`x`

Compiler

Compiled 46 to 34 computations (26.1% saved)

bsearch30.0ms (0.4%)

Memory

-1.3MiB live, 41.3MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
12.0ms	4.62280077899785e+29	3.6470205486799382e+31
15.0ms	-4.391393921746576e-85	-9.627589513487334e-102

Samples

17.0ms

272×

valid

Compiler

Compiled 339 to 254 computations (25.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-sqrt: 4.0ms (37.8% of total)

ival-mult: 3.0ms (28.4% of total)

ival-div: 2.0ms (18.9% of total)

ival-add: 1.0ms (9.5% of total)

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

exact: 0.0ms (0% of total)

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

simplify7.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	66
1	32	66

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 x #s(literal -7524142493253561/17498005798264095394980017816940970922825355447145699491406164851279623993595007385788105416184430592 binary64)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) (if (<=.f64 x #s(literal 15500000000000001011899126775808 binary64)) #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) x))

Outputs
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 z) y x))
(if (<=.f64 x #s(literal -7524142493253561/17498005798264095394980017816940970922825355447145699491406164851279623993595007385788105416184430592 binary64)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (.f64 #s(literal 1/2 binary64) x)) (if (<=.f64 x #s(literal 15500000000000001011899126775808 binary64)) #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))))
(if (<=.f64 x #s(literal -7524142493253561/17498005798264095394980017816940970922825355447145699491406164851279623993595007385788105416184430592 binary64)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (.f64 #s(literal 1/2 binary64) x)) (if (<=.f64 x #s(literal 15500000000000001011899126775808 binary64)) #s(approx ( (/ 1 2) (+ x (* y (sqrt z)))) (.f64 (.f64 y (sqrt.f64 z)) #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 #s(literal 1/2 binary64) x))

soundness761.0ms (10.9%)

Memory

11.5MiB live, 209.1MiB 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 97 to 48 computations (50.5% saved)

preprocess27.0ms (0.4%)

Memory: -17.7MiB live, 60.0MiB allocated
Compiler: Compiled 100 to 52 computations (48% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	25	145
0	44	139
1	67	139
2	103	139
3	177	139
4	276	139
5	276	139
6	327	139
7	327	139
8	329	139
9	334	139
10	334	139
0	334	139

Iter	Nodes	Cost
0	25	172
0	38	172
1	52	166
2	54	166
3	65	166
4	73	166
5	89	166
6	99	166
7	107	166
8	109	166
0	109	158

Iter	Nodes	Cost
0	25	145
0	44	139
1	67	139
2	103	139
3	177	139
4	276	139
5	276	139
6	327	139
7	327	139
8	329	139
9	334	139
10	334	139
0	334	139

Iter	Nodes	Cost
0	25	172
0	38	172
1	52	166
2	54	166
3	65	166
4	73	166
5	89	166
6	99	166
7	107	166
8	109	166
0	109	158

start0.0ms (0%)

analyze74.0ms (1.1%)

sample1.3s (18.9%)

explain99.0ms (1.4%)

preprocess78.0ms (1.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize24.0ms (0.3%)

series9.0ms (0.1%)

simplify162.0ms (2.3%)

rewrite225.0ms (3.2%)

eval52.0ms (0.7%)

prune58.0ms (0.8%)

simplify10.0ms (0.1%)

localize119.0ms (1.7%)

series252.0ms (3.6%)

simplify154.0ms (2.2%)

rewrite232.0ms (3.3%)

eval325.0ms (4.6%)

prune642.0ms (9.2%)

simplify14.0ms (0.2%)

localize80.0ms (1.1%)

series49.0ms (0.7%)

simplify164.0ms (2.3%)

rewrite215.0ms (3.1%)

eval595.0ms (8.5%)

prune363.0ms (5.2%)

simplify8.0ms (0.1%)

localize50.0ms (0.7%)

series53.0ms (0.8%)

simplify141.0ms (2%)

rewrite172.0ms (2.5%)

eval164.0ms (2.3%)

prune182.0ms (2.6%)

regimes64.0ms (0.9%)

regimes16.0ms (0.2%)

regimes12.0ms (0.2%)

bsearch30.0ms (0.4%)

simplify7.0ms (0.1%)

soundness761.0ms (10.9%)

preprocess27.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	25	145
0	44	139
1	67	139
2	103	139
3	177	139
4	276	139
5	276	139
6	327	139
7	327	139
8	329	139
9	334	139
10	334	139
0	334	139

Iter	Nodes	Cost
0	25	172
0	38	172
1	52	166
2	54	166
3	65	166
4	73	166
5	89	166
6	99	166
7	107	166
8	109	166
0	109	158