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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze42.0ms (0.5%)

Memory

28.6MiB live, 67.0MiB 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
50%	49.9%	49.9%	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
75%	74.9%	25%	0.1%	0%	0%	0%	6
75%	74.9%	25%	0.1%	0%	0%	0%	7
75%	74.9%	25%	0.1%	0%	0%	0%	8
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	9
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	10
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	11
93.8%	93.6%	6.2%	0.1%	0%	0%	0%	12

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample927.0ms (11.9%)

Memory

27.8MiB live, 1 351.9MiB allocated

Samples

638.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 448.0ms

ival-mult: 280.0ms (62.5% of total)

ival-div: 56.0ms (12.5% of total)

ival-sub: 54.0ms (12.1% of total)

ival-add: 42.0ms (9.4% of total)

ival-true: 6.0ms (1.3% of total)

exact: 5.0ms (1.1% of total)

ival-assert: 3.0ms (0.7% of total)

Bogosity

explain130.0ms (1.7%)

Memory

-8.1MiB live, 248.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
64	-	-	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`
13	-	-	`(-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
0	-	-	`z`
0	-	-	`(*.f64 x x)`
0	-	-	`(*.f64 y #s(literal 2 binary64))`
0	-	-	`(+.f64 (.f64 x x) (.f64 y y))`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`y`
0	-	-	`(*.f64 z z)`
0	-	-	`(*.f64 y y)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`	o/n	63	0
↳	`(-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	153
↳	`(*.f64 y y)`	overflow	64
↳	`(*.f64 x x)`	overflow	69
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	116
↳	`(*.f64 z z)`	overflow	50
`-.f64`	`(-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	nan-rescue	13	0
↳	`(*.f64 y y)`	overflow	64
↳	`(*.f64 x x)`	overflow	69
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	116
↳	`(*.f64 z z)`	overflow	50
`/.f64`	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`	u/n	1	0
↳	`(-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	underflow	1
↳	`(*.f64 y y)`	underflow	61
↳	`(*.f64 x x)`	underflow	57
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	16
↳	`(*.f64 z z)`	underflow	55

Confusion

	Predicted +	Predicted -
+	72	0
-	0	184

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	72	0	0
-	0	0	184

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	184
1	67
2	5

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

40.0ms

512×

valid

Compiler

Compiled 120 to 37 computations (69.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-mult: 14.0ms (61.6% of total)

ival-div: 3.0ms (13.2% of total)

ival-sub: 2.0ms (8.8% of total)

ival-add: 2.0ms (8.8% of total)

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

exact: 0.0ms (0% of total)

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

preprocess504.0ms (6.5%)

Memory

-0.1MiB live, 192.3MiB allocated

Algorithm

1×	egg-herbie

Rules

12 972×	`lower-fma.f64`
12 972×	`lower-fma.f32`
3 732×	`lower-*.f32`
3 724×	`lower-*.f64`
2 414×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	138
1	147	135
2	489	135
3	2191	135
4	6834	117
0	11	15
0	18	15
1	32	15
2	69	15
3	136	15
4	295	15
5	630	15
6	1505	13
7	3475	13
8	7859	13
0	8033	12

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs z)

(abs x)

(negabs y)

Compiler

Compiled 18 to 11 computations (38.9% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	73.5%	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))

Compiler

Compiled 18 to 11 computations (38.9% saved)

simplify161.0ms (2.1%)

Memory

15.1MiB live, 165.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	128	(+.f64 (.f64 x x) (.f64 y y))
cost-diff	128	(-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
cost-diff	192	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))

Rules

12 972×	`lower-fma.f64`
12 972×	`lower-fma.f32`
3 732×	`lower-*.f32`
3 724×	`lower-*.f64`
2 414×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	49
0	18	49
1	32	49
2	69	49
3	136	49
4	295	49
5	630	49
6	1505	47
7	3475	47
8	7859	47
0	8033	44

Stop Event

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

Calls

Call 1

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

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

localize197.0ms (2.5%)

Memory

-0.5MiB live, 48.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (.f64 x x) (.f64 y y))
accuracy	2.9062376149812352	(-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
accuracy	14.837392511548675	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))

Samples

190.0ms

256×

valid

Compiler

Compiled 51 to 13 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-mult: 24.0ms (85.2% of total)

ival-div: 2.0ms (7.1% of total)

ival-sub: 1.0ms (3.5% of total)

ival-add: 1.0ms (3.5% of total)

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

exact: 0.0ms (0% of total)

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

series37.0ms (0.5%)

Memory

-21.7MiB live, 15.9MiB allocated

Counts

4 → 108

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
26.0ms	z	@	0	((/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (- (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (* x x))
1.0ms	y	@	inf	((/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (- (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (* x x))
1.0ms	z	@	inf	((/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (- (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (* x x))
1.0ms	x	@	inf	((/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (- (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (* x x))
1.0ms	x	@	0	((/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (- (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (* x x))

simplify153.0ms (2%)

Memory

-18.3MiB live, 153.4MiB allocated

Algorithm

1×	egg-herbie

Rules

7 488×	`lower-fma.f64`
7 488×	`lower-fma.f32`
4 752×	`lower-*.f64`
4 752×	`lower-*.f32`
1 676×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	1170
1	196	1170
2	566	1168
3	2183	1028
4	6030	1004
0	8152	918

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

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

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

rewrite196.0ms (2.5%)

Memory

16.6MiB live, 239.6MiB allocated

Rules

5 846×	`lower-*.f32`
5 838×	`lower-*.f64`
5 096×	`lower-fma.f64`
5 096×	`lower-fma.f32`
4 708×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
0	18	36
1	68	36
2	569	36
0	8301	33

Stop Event

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

Counts

4 → 522

Calls

Call 1

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

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

eval94.0ms (1.2%)

Memory: 25.0MiB live, 149.7MiB allocated
Compiler: Compiled 26 501 to 1 601 computations (94% saved)

prune186.0ms (2.4%)

Memory

-20.6MiB live, 238.3MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	621	9	630
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	622	9	631

Accuracy

100.0%

Counts

631 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.2%	(/.f64 (-.f64 (.f64 #s(literal 2 binary64) y) (.f64 (/.f64 (.f64 #s(literal 2 binary64) y) (fma.f64 y y (.f64 x x))) (.f64 z z))) (.f64 (/.f64 (.f64 #s(literal 2 binary64) y) (fma.f64 y y (.f64 x x))) (*.f64 #s(literal 2 binary64) y)))
▶	34.1%	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))
▶	75.2%	(/.f64 #s(literal 1/2 binary64) (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x))))
▶	75.2%	(.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) y))
	66.9%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)))
	69.1%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 (.f64 (-.f64 x z) #s(literal 1/2 binary64)) y) (+.f64 z x)))
	32.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64)))
▶	62.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (-.f64 y (/.f64 (.f64 z z) y)) #s(literal 1/2 binary64)))
▶	32.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 y #s(literal 1/2 binary64)))

Compiler

Compiled 278 to 152 computations (45.3% saved)

simplify182.0ms (2.3%)

Memory

-24.5MiB live, 165.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

13 630×	`lower-fma.f32`
13 628×	`lower-fma.f64`
3 264×	`lower--.f32`
3 260×	`lower--.f64`
2 808×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	208
0	46	208
1	75	204
2	152	204
3	405	204
4	1187	204
5	3145	200
6	6580	200
0	8489	196

Stop Event

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

Calls

Call 1

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

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

localize80.0ms (1%)

Memory

37.9MiB live, 111.6MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y z)
accuracy	0	(*.f64 x x)
accuracy	0.9999889904222409	(fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x))
accuracy	14.892080011548675	(.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) y))
accuracy	0	(.f64 (-.f64 y (/.f64 (.f64 z z) y)) #s(literal 1/2 binary64))
accuracy	0	(*.f64 z z)
accuracy	4.7994579106976545	(/.f64 (*.f64 z z) y)
accuracy	22.22228226812619	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (-.f64 y (/.f64 (.f64 z z) y)) #s(literal 1/2 binary64)))
accuracy	0	(*.f64 y #s(literal 2 binary64))
accuracy	0	(*.f64 x x)
accuracy	14.837392511548675	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))
accuracy	38.28814771590722	#s(approx (- (+ (* x x) (* y y)) (* z z)) (*.f64 x x))
accuracy	0	(*.f64 y #s(literal 1/2 binary64))
accuracy	43.02568679821428	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 y #s(literal 1/2 binary64)))
accuracy	0	(*.f64 x x)
accuracy	0.1484375	(/.f64 #s(literal 1/2 binary64) (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x))))
accuracy	0.9999889904222409	(fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x))
accuracy	15.385910105995604	(/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)))

Samples

64.0ms

256×

valid

Compiler

Compiled 193 to 26 computations (86.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-mult: 33.0ms (68.3% of total)

ival-div: 8.0ms (16.6% of total)

ival-add: 4.0ms (8.3% of total)

ival-sub: 3.0ms (6.2% of total)

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

exact: 0.0ms (0% of total)

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

series65.0ms (0.8%)

Memory

-8.2MiB live, 72.1MiB allocated

Counts

17 → 456

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
24.0ms	z	@	inf	((/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ (* (+ y z) (- y z)) (* x x)) (+ y z) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* y 1/2) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (- (+ (* x x) (* y y)) (* z z)) (* x x) (* y 2) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (- y (/ (* z z) y)) 1/2) (- y (/ (* z z) y)) (/ (* z z) y) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (- y z) (* z z))
6.0ms	y	@	-inf	((/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ (* (+ y z) (- y z)) (* x x)) (+ y z) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* y 1/2) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (- (+ (* x x) (* y y)) (* z z)) (* x x) (* y 2) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (- y (/ (* z z) y)) 1/2) (- y (/ (* z z) y)) (/ (* z z) y) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (- y z) (* z z))
3.0ms	y	@	inf	((/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ (* (+ y z) (- y z)) (* x x)) (+ y z) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* y 1/2) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (- (+ (* x x) (* y y)) (* z z)) (* x x) (* y 2) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (- y (/ (* z z) y)) 1/2) (- y (/ (* z z) y)) (/ (* z z) y) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (- y z) (* z z))
3.0ms	y	@	0	((/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ (* (+ y z) (- y z)) (* x x)) (+ y z) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* y 1/2) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (- (+ (* x x) (* y y)) (* z z)) (* x x) (* y 2) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (- y (/ (* z z) y)) 1/2) (- y (/ (* z z) y)) (/ (* z z) y) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (- y z) (* z z))
3.0ms	z	@	0	((/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ (* (+ y z) (- y z)) (* x x)) (+ y z) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* y 1/2) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (- (+ (* x x) (* y y)) (* z z)) (* x x) (* y 2) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (- y (/ (* z z) y)) 1/2) (- y (/ (* z z) y)) (/ (* z z) y) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (- y z) (* z z))

simplify138.0ms (1.8%)

Memory

11.4MiB live, 132.1MiB allocated

Algorithm

1×	egg-herbie

Rules

3 364×	`lower-fma.f64`
3 364×	`lower-fma.f32`
3 026×	`lower-*.f64`
3 026×	`lower-*.f32`
1 364×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	438	6168
1	1460	5526
2	6137	5290
0	8365	5014

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 444

Calls

Call 1

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

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

rewrite266.0ms (3.4%)

Memory

-22.5MiB live, 333.5MiB allocated

Rules

4 980×	`lower-/.f32`
4 970×	`lower-/.f64`
4 396×	`lower-fma.f32`
4 394×	`lower-fma.f64`
3 962×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	167
0	46	167
1	173	163
2	1433	163
0	8496	163

Stop Event

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

Counts

17 → 926

Calls

Call 1

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

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

eval250.0ms (3.2%)

Memory: 34.9MiB live, 406.3MiB allocated
Compiler: Compiled 52 528 to 2 808 computations (94.7% saved)

prune293.0ms (3.7%)

Memory

9.2MiB live, 445.6MiB allocated

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	1 713	6	1 719
Fresh	1	3	4
Picked	3	2	5
Done	0	0	0
Total	1 717	11	1 728

Accuracy

100.0%

Counts

1 728 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.2%	(/.f64 (-.f64 (.f64 #s(literal 2 binary64) y) (.f64 (/.f64 (.f64 #s(literal 2 binary64) y) (fma.f64 y y (.f64 x x))) (.f64 z z))) (.f64 (/.f64 (.f64 #s(literal 2 binary64) y) (fma.f64 y y (.f64 x x))) (*.f64 #s(literal 2 binary64) y)))
	65.4%	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 (+.f64 x z) (-.f64 x z))) (.f64 y #s(literal 2 binary64)))
✓	34.1%	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))
▶	34.1%	(/.f64 #s(literal 1/2 binary64) (/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (*.f64 x x))))
	34.1%	(.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ ( x x) (* y y)) (* z z)) (*.f64 x x)))
▶	32.7%	(.f64 #s(approx (+ ( (+ y z) (- y z)) (* x x)) (*.f64 (neg.f64 z) z)) (/.f64 #s(literal 1/2 binary64) y))
▶	66.9%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)))
	65.2%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (neg.f64 z) (/.f64 z y) y) #s(literal 1/2 binary64)))
▶	32.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64)))
▶	65.2%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (-.f64 y (/.f64 z (/.f64 y z))) #s(literal 1/2 binary64)))
✓	32.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 y #s(literal 1/2 binary64)))

Compiler

Compiled 286 to 160 computations (44.1% saved)

simplify157.0ms (2%)

Memory

12.6MiB live, 173.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 y (/.f64 z (/.f64 y z)))
cost-diff	0	(*.f64 (-.f64 y (/.f64 z (/.f64 y z))) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (-.f64 y (/.f64 z (/.f64 y z))) #s(literal 1/2 binary64)))
cost-diff	384	(/.f64 z (/.f64 y z))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (* (+ y z) (- y z)) (* x x)) (*.f64 x x))
cost-diff	0	(/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (*.f64 x x)))
cost-diff	384	(/.f64 #s(literal 1/2 binary64) (/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (*.f64 x x))))
cost-diff	0	(neg.f64 z)
cost-diff	0	(*.f64 (neg.f64 z) z)
cost-diff	0	#s(approx (+ (* (+ y z) (- y z)) (* x x)) (*.f64 (neg.f64 z) z))
cost-diff	0	(.f64 #s(approx (+ ( (+ y z) (- y z)) (* x x)) (*.f64 (neg.f64 z) z)) (/.f64 #s(literal 1/2 binary64) y))
cost-diff	0	(*.f64 z z)
cost-diff	0	(/.f64 (*.f64 z z) y)
cost-diff	0	(.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64))
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64)))
cost-diff	0	(/.f64 x y)
cost-diff	0	(fma.f64 (/.f64 x y) x y)
cost-diff	0	(*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)))

Rules

11 794×	`lower-fma.f32`
11 792×	`lower-fma.f64`
3 102×	`lower-*.f32`
3 088×	`lower-*.f64`
1 946×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	242
0	57	242
1	95	242
2	183	242
3	404	242
4	942	242
5	1753	236
6	3618	236
0	8300	228

Stop Event

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

Calls

Call 1

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

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

localize143.0ms (1.8%)

Memory

-44.5MiB live, 146.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 y (/.f64 z (/.f64 y z)))
accuracy	0	(*.f64 (-.f64 y (/.f64 z (/.f64 y z))) #s(literal 1/2 binary64))
accuracy	0.15234375	(/.f64 z (/.f64 y z))
accuracy	22.22228226812619	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (-.f64 y (/.f64 z (/.f64 y z))) #s(literal 1/2 binary64)))
accuracy	0	(*.f64 x x)
accuracy	0.1484375	(/.f64 #s(literal 1/2 binary64) (/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (*.f64 x x))))
accuracy	15.385910105995604	(/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (*.f64 x x)))
accuracy	38.28814771590722	#s(approx (+ (* (+ y z) (- y z)) (* x x)) (*.f64 x x))
accuracy	0	(*.f64 (neg.f64 z) z)
accuracy	0	(neg.f64 z)
accuracy	14.892080011548675	(.f64 #s(approx (+ ( (+ y z) (- y z)) (* x x)) (*.f64 (neg.f64 z) z)) (/.f64 #s(literal 1/2 binary64) y))
accuracy	42.3038162201088	#s(approx (+ (* (+ y z) (- y z)) (* x x)) (*.f64 (neg.f64 z) z))
accuracy	0	(.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64))
accuracy	0	(*.f64 z z)
accuracy	4.7994579106976545	(/.f64 (*.f64 z z) y)
accuracy	42.374609568214254	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64)))
accuracy	0	(/.f64 x y)
accuracy	0	(*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))
accuracy	0.06640625	(fma.f64 (/.f64 x y) x y)
accuracy	21.161736521087406	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)))

Samples

125.0ms

256×

valid

Compiler

Compiled 197 to 35 computations (82.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 105.0ms

ival-mult: 48.0ms (45.5% of total)

ival-div: 47.0ms (44.6% of total)

ival-add: 4.0ms (3.8% of total)

ival-sub: 3.0ms (2.8% of total)

ival-neg: 1.0ms (0.9% of total)

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

exact: 0.0ms (0% of total)

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

series62.0ms (0.8%)

Memory

-9.4MiB live, 72.2MiB allocated

Counts

20 → 528

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
12.0ms	y	@	-inf	((/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ x y) x) y) 1/2) (+ (* (/ x y) x) y) (/ x y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (/ (* z z) y) -1/2) (/ (* z z) y) (* z z) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (+ (* (+ y z) (- y z)) (* x x)) (* (neg z) z) (neg z) (/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ (* (+ y z) (- y z)) (* x x)) (* x x) (/ z (/ y z)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (- y (/ z (/ y z))) 1/2) (- y (/ z (/ y z))))
2.0ms	z	@	inf	((/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ x y) x) y) 1/2) (+ (* (/ x y) x) y) (/ x y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (/ (* z z) y) -1/2) (/ (* z z) y) (* z z) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (+ (* (+ y z) (- y z)) (* x x)) (* (neg z) z) (neg z) (/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ (* (+ y z) (- y z)) (* x x)) (* x x) (/ z (/ y z)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (- y (/ z (/ y z))) 1/2) (- y (/ z (/ y z))))
2.0ms	y	@	inf	((/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ x y) x) y) 1/2) (+ (* (/ x y) x) y) (/ x y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (/ (* z z) y) -1/2) (/ (* z z) y) (* z z) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (+ (* (+ y z) (- y z)) (* x x)) (* (neg z) z) (neg z) (/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ (* (+ y z) (- y z)) (* x x)) (* x x) (/ z (/ y z)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (- y (/ z (/ y z))) 1/2) (- y (/ z (/ y z))))
2.0ms	z	@	-inf	((/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ x y) x) y) 1/2) (+ (* (/ x y) x) y) (/ x y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (/ (* z z) y) -1/2) (/ (* z z) y) (* z z) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (+ (* (+ y z) (- y z)) (* x x)) (* (neg z) z) (neg z) (/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ (* (+ y z) (- y z)) (* x x)) (* x x) (/ z (/ y z)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (- y (/ z (/ y z))) 1/2) (- y (/ z (/ y z))))
2.0ms	x	@	inf	((/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ x y) x) y) 1/2) (+ (* (/ x y) x) y) (/ x y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (/ (* z z) y) -1/2) (/ (* z z) y) (* z z) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (+ (* (+ y z) (- y z)) (* x x)) (* (neg z) z) (neg z) (/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ (* (+ y z) (- y z)) (* x x)) (* x x) (/ z (/ y z)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (- y (/ z (/ y z))) 1/2) (- y (/ z (/ y z))))

simplify151.0ms (1.9%)

Memory

34.9MiB live, 106.4MiB allocated

Algorithm

1×	egg-herbie

Rules

3 474×	`lower-fma.f64`
3 474×	`lower-fma.f32`
3 040×	`lower-*.f64`
3 040×	`lower-*.f32`
1 458×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	427	6430
1	1437	6012
2	6032	5834
0	8589	5551

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 522

Calls

Call 1

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

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

rewrite334.0ms (4.3%)

Memory

-5.0MiB live, 263.2MiB allocated

Rules

5 374×	`lower-/.f32`
5 360×	`lower-/.f64`
4 742×	`lower-fma.f32`
4 740×	`lower-fma.f64`
4 070×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	221
0	57	221
1	213	221
2	1616	221
0	8330	213

Stop Event

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

Counts

20 → 403

Calls

Call 1

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

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

eval196.0ms (2.5%)

Memory: -9.5MiB live, 233.9MiB allocated
Compiler: Compiled 14 722 to 1 257 computations (91.5% saved)

prune181.0ms (2.3%)

Memory

10.4MiB live, 173.6MiB allocated

Pruning

11 alts after pruning (6 fresh and 5 done)

	Pruned	Kept	Total
New	921	4	925
Fresh	2	2	4
Picked	2	3	5
Done	0	2	2
Total	925	11	936

Accuracy

100.0%

Counts

936 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	65.4%	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 (+.f64 x z) (-.f64 x z))) (.f64 y #s(literal 2 binary64)))
✓	34.1%	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))
✓	34.1%	(/.f64 #s(literal 1/2 binary64) (/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (*.f64 x x))))
▶	34.1%	(.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ ( x x) (* y y)) (* z z)) (*.f64 x x)))
▶	65.2%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 z y) (neg.f64 z) y) #s(literal 1/2 binary64)))
✓	66.9%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)))
▶	66.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y x)) x y) #s(literal 1/2 binary64)))
✓	32.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64)))
▶	33.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (/.f64 z (/.f64 y z)) #s(literal -1/2 binary64)))
▶	33.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64)))
✓	32.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 y #s(literal 1/2 binary64)))

Compiler

Compiled 202 to 127 computations (37.1% saved)

simplify170.0ms (2.2%)

Memory

3.0MiB live, 76.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 y z)
cost-diff	0	(*.f64 (/.f64 z (/.f64 y z)) #s(literal -1/2 binary64))
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (/.f64 z (/.f64 y z)) #s(literal -1/2 binary64)))
cost-diff	384	(/.f64 z (/.f64 y z))
cost-diff	0	(/.f64 z y)
cost-diff	0	(fma.f64 (/.f64 z y) (neg.f64 z) y)
cost-diff	0	(*.f64 (fma.f64 (/.f64 z y) (neg.f64 z) y) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 z y) (neg.f64 z) y) #s(literal 1/2 binary64)))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (- (+ (* x x) (* y y)) (* z z)) (*.f64 x x))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ ( x x) (* y y)) (* z z)) (*.f64 x x)))
cost-diff	0	(/.f64 z y)
cost-diff	0	(*.f64 (/.f64 z y) z)
cost-diff	0	(.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64))
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64)))
cost-diff	0	(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y x)) x y)
cost-diff	0	(*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y x)) x y) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y x)) x y) #s(literal 1/2 binary64)))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 y x))

Rules

7 866×	`lower-fma.f32`
7 862×	`lower-fma.f64`
2 924×	`lower-*.f32`
2 912×	`lower-*.f64`
1 588×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	230
0	53	230
1	93	222
2	186	222
3	361	222
4	714	222
5	1294	214
6	2666	214
7	6148	214
0	8072	208

Stop Event

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

Calls

Call 1

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

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

localize125.0ms (1.6%)

Memory

12.2MiB live, 84.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 y z)
accuracy	0	(*.f64 (/.f64 z (/.f64 y z)) #s(literal -1/2 binary64))
accuracy	0.15234375	(/.f64 z (/.f64 y z))
accuracy	42.374609568214254	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (/.f64 z (/.f64 y z)) #s(literal -1/2 binary64)))
accuracy	0	(*.f64 (fma.f64 (/.f64 z y) (neg.f64 z) y) #s(literal 1/2 binary64))
accuracy	0	(neg.f64 z)
accuracy	0.0703125	(fma.f64 (/.f64 z y) (neg.f64 z) y)
accuracy	22.22228226812619	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 z y) (neg.f64 z) y) #s(literal 1/2 binary64)))
accuracy	0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0	(*.f64 x x)
accuracy	14.892080011548675	(.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ ( x x) (* y y)) (* z z)) (*.f64 x x)))
accuracy	38.28814771590722	#s(approx (- (+ (* x x) (* y y)) (* z z)) (*.f64 x x))
accuracy	0	(/.f64 z y)
accuracy	0	(.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64))
accuracy	0.11328125	(*.f64 (/.f64 z y) z)
accuracy	42.374609568214254	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64)))
accuracy	0	(*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y x)) x y) #s(literal 1/2 binary64))
accuracy	0.06640625	(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y x)) x y)
accuracy	0.5468271664678908	(/.f64 #s(literal 1 binary64) (/.f64 y x))
accuracy	21.161736521087406	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y x)) x y) #s(literal 1/2 binary64)))

Samples

107.0ms

256×

valid

Compiler

Compiled 191 to 33 computations (82.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-add: 25.0ms (44.3% of total)

ival-mult: 18.0ms (31.9% of total)

ival-div: 11.0ms (19.5% of total)

ival-sub: 1.0ms (1.8% of total)

exact: 1.0ms (1.8% of total)

ival-neg: 1.0ms (1.8% of total)

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

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

series68.0ms (0.9%)

Memory

-3.0MiB live, 46.4MiB allocated

Counts

20 → 516

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
37.0ms	y	@	0	((/ 1 (/ y x)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ 1 (/ y x)) x) y) 1/2) (+ (* (/ 1 (/ y x)) x) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* (/ z y) z) -1/2) (* (/ z y) z) (/ z y) (* (/ 1/2 y) (- (+ (* x x) (* y y)) (* z z))) (/ 1/2 y) (- (+ (* x x) (* y y)) (* z z)) (* x x) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ z y) (neg z)) y) 1/2) (+ (* (/ z y) (neg z)) y) (/ z (/ y z)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (/ z (/ y z)) -1/2) (/ y z) (neg z))
3.0ms	y	@	-inf	((/ 1 (/ y x)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ 1 (/ y x)) x) y) 1/2) (+ (* (/ 1 (/ y x)) x) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* (/ z y) z) -1/2) (* (/ z y) z) (/ z y) (* (/ 1/2 y) (- (+ (* x x) (* y y)) (* z z))) (/ 1/2 y) (- (+ (* x x) (* y y)) (* z z)) (* x x) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ z y) (neg z)) y) 1/2) (+ (* (/ z y) (neg z)) y) (/ z (/ y z)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (/ z (/ y z)) -1/2) (/ y z) (neg z))
3.0ms	y	@	inf	((/ 1 (/ y x)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ 1 (/ y x)) x) y) 1/2) (+ (* (/ 1 (/ y x)) x) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* (/ z y) z) -1/2) (* (/ z y) z) (/ z y) (* (/ 1/2 y) (- (+ (* x x) (* y y)) (* z z))) (/ 1/2 y) (- (+ (* x x) (* y y)) (* z z)) (* x x) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ z y) (neg z)) y) 1/2) (+ (* (/ z y) (neg z)) y) (/ z (/ y z)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (/ z (/ y z)) -1/2) (/ y z) (neg z))
2.0ms	z	@	-inf	((/ 1 (/ y x)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ 1 (/ y x)) x) y) 1/2) (+ (* (/ 1 (/ y x)) x) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* (/ z y) z) -1/2) (* (/ z y) z) (/ z y) (* (/ 1/2 y) (- (+ (* x x) (* y y)) (* z z))) (/ 1/2 y) (- (+ (* x x) (* y y)) (* z z)) (* x x) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ z y) (neg z)) y) 1/2) (+ (* (/ z y) (neg z)) y) (/ z (/ y z)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (/ z (/ y z)) -1/2) (/ y z) (neg z))
2.0ms	z	@	inf	((/ 1 (/ y x)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ 1 (/ y x)) x) y) 1/2) (+ (* (/ 1 (/ y x)) x) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* (/ z y) z) -1/2) (* (/ z y) z) (/ z y) (* (/ 1/2 y) (- (+ (* x x) (* y y)) (* z z))) (/ 1/2 y) (- (+ (* x x) (* y y)) (* z z)) (* x x) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ z y) (neg z)) y) 1/2) (+ (* (/ z y) (neg z)) y) (/ z (/ y z)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (/ z (/ y z)) -1/2) (/ y z) (neg z))

simplify210.0ms (2.7%)

Memory

-6.1MiB live, 196.5MiB allocated

Algorithm

1×	egg-herbie

Rules

13 640×	`lower-fma.f64`
13 640×	`lower-fma.f32`
4 754×	`lower-*.f64`
4 754×	`lower-*.f32`
2 046×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	123	5245
1	332	5245
2	903	5091
3	3192	4437
4	6469	4437
0	8258	4191

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 510

Calls

Call 1

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

rewrite232.0ms (3%)

Memory

6.6MiB live, 159.4MiB allocated

Rules

5 664×	`lower-fma.f32`
5 660×	`lower-fma.f64`
4 220×	`lower-*.f32`
4 208×	`lower-*.f64`
3 930×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	208
0	53	208
1	179	200
2	1266	200
0	8293	194

Stop Event

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

Counts

20 → 678

Calls

Call 1

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

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

eval245.0ms (3.1%)

Memory: 9.9MiB live, 229.4MiB allocated
Compiler: Compiled 17 638 to 1 472 computations (91.7% saved)

prune229.0ms (2.9%)

Memory

-12.6MiB live, 314.5MiB allocated

Pruning

11 alts after pruning (1 fresh and 10 done)

	Pruned	Kept	Total
New	1 244	0	1 244
Fresh	0	1	1
Picked	0	5	5
Done	0	5	5
Total	1 244	11	1 255

Accuracy

100.0%

Counts

1 255 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	65.4%	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 (+.f64 x z) (-.f64 x z))) (.f64 y #s(literal 2 binary64)))
✓	34.1%	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))
✓	34.1%	(/.f64 #s(literal 1/2 binary64) (/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (*.f64 x x))))
✓	34.1%	(.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ ( x x) (* y y)) (* z z)) (*.f64 x x)))
✓	65.2%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 z y) (neg.f64 z) y) #s(literal 1/2 binary64)))
✓	66.9%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)))
✓	66.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y x)) x y) #s(literal 1/2 binary64)))
✓	32.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64)))
✓	33.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (/.f64 z (/.f64 y z)) #s(literal -1/2 binary64)))
✓	33.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64)))
✓	32.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 y #s(literal 1/2 binary64)))

Compiler

Compiled 351 to 147 computations (58.1% saved)

regimes40.0ms (0.5%)

Memory

0.6MiB live, 85.0MiB allocated

Counts

20 → 2

Calls

Call 1

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

Outputs

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

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

Calls

6 calls:

8.0ms	(*.f64 x x)
8.0ms	y
6.0ms	x
6.0ms	z
6.0ms	(*.f64 z z)

Results

Accuracy	Segments	Branch
92.0%	3	`x`
95.0%	2	`y`
88.6%	3	`z`
97.4%	2	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`
92.0%	3	`(*.f64 x x)`
88.6%	3	`(*.f64 z z)`

Compiler

Compiled 42 to 28 computations (33.3% saved)

regimes5.0ms (0.1%)

Memory

11.7MiB live, 11.7MiB allocated

Counts

14 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

4.0ms

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

Results

Accuracy	Segments	Branch
97.4%	2	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`

Compiler

Compiled 18 to 11 computations (38.9% saved)

regimes3.0ms (0%)

Memory

8.1MiB live, 8.1MiB allocated

Counts

8 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

3.0ms

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

Results

Accuracy	Segments	Branch
97.1%	2	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`

Compiler

Compiled 18 to 11 computations (38.9% saved)

regimes16.0ms (0.2%)

Memory

-2.4MiB live, 34.9MiB allocated

Counts

5 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

6 calls:

4.0ms	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))
2.0ms	y
2.0ms	x
2.0ms	z
2.0ms	(*.f64 z z)

Results

Accuracy	Segments	Branch
59.6%	5	`z`
59.6%	5	`(*.f64 z z)`
61.0%	3	`x`
61.0%	3	`(*.f64 x x)`
61.4%	3	`y`
71.3%	3	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`

Compiler

Compiled 42 to 28 computations (33.3% saved)

regimes4.0ms (0.1%)

Memory

-31.6MiB live, 5.8MiB allocated

Counts

4 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

1 calls:

2.0ms

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

Results

Accuracy	Segments	Branch
71.3%	3	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`

Compiler

Compiled 18 to 11 computations (38.9% saved)

regimes2.0ms (0%)

Memory

5.1MiB live, 5.1MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

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

Calls

1 calls:

2.0ms

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

Results

Accuracy	Segments	Branch
62.9%	2	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`

Compiler

Compiled 18 to 11 computations (38.9% saved)

regimes8.0ms (0.1%)

Memory

30.8MiB live, 30.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
32.8%	1	`z`
32.8%	1	`(*.f64 z z)`
32.8%	1	`x`
32.8%	1	`(*.f64 x x)`
32.8%	1	`y`
32.8%	1	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`

Compiler

Compiled 42 to 28 computations (33.3% saved)

bsearch0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.879397853280463e-109	0.0

Compiler

Compiled 21 to 17 computations (19% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.879397853280463e-109	0.0

Compiler

Compiled 21 to 17 computations (19% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.879397853280463e-109	0.0

Compiler

Compiled 21 to 17 computations (19% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	3.277406894935678e+146	9.569570685742118e+149
0.0ms	-3.879397853280463e-109	0.0

Compiler

Compiled 21 to 17 computations (19% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	3.277406894935678e+146	9.569570685742118e+149
0.0ms	-3.879397853280463e-109	0.0

Compiler

Compiled 21 to 17 computations (19% saved)

bsearch6.0ms (0.1%)

Memory

-37.7MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
5.0ms	-3.879397853280463e-109	0.0

Compiler

Compiled 21 to 17 computations (19% saved)

simplify10.0ms (0.1%)

Memory

26.0MiB live, 26.0MiB allocated

Algorithm

1×	egg-herbie

Rules

26×	`*-commutative_binary64`
16×	`+-commutative_binary64`
14×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	472
1	74	472
2	86	472
3	96	472
4	102	472
5	105	472
6	106	472

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (-.f64 y (/.f64 z (/.f64 y z))) #s(literal 1/2 binary64))) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 (neg.f64 z) (/.f64 z y) y) #s(literal 1/2 binary64))) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64))) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64))) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 499999999999999988998191202828830087182411944733900540386126622484631969614553746213463024711630256984884134207768538734419216153365573197681917952 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 y #s(literal 1/2 binary64))) (/.f64 #s(approx (- (+ ( x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64))) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 499999999999999988998191202828830087182411944733900540386126622484631969614553746213463024711630256984884134207768538734419216153365573197681917952 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 y #s(literal 1/2 binary64))) (.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ (* x x) (* y y)) (* z z)) (*.f64 x x)))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64))) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 y #s(literal 1/2 binary64))))
#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 y #s(literal 1/2 binary64)))

Outputs
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (-.f64 y (/.f64 z (/.f64 y z))) #s(literal 1/2 binary64))) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) (-.f64 y (/.f64 z (/.f64 y z))))) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 (neg.f64 z) (/.f64 z y) y) #s(literal 1/2 binary64))) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 (neg.f64 z) (/.f64 z y) y) #s(literal 1/2 binary64))) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64))) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 z y) z))) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64))) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 499999999999999988998191202828830087182411944733900540386126622484631969614553746213463024711630256984884134207768538734419216153365573197681917952 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 y #s(literal 1/2 binary64))) (/.f64 #s(approx (- (+ ( x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 z y) z))) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal 499999999999999988998191202828830087182411944733900540386126622484631969614553746213463024711630256984884134207768538734419216153365573197681917952 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) (/.f64 #s(approx (- (+ ( x x) (* y y)) (* z z)) (.f64 x x)) (.f64 #s(literal 2 binary64) y))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64))) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 499999999999999988998191202828830087182411944733900540386126622484631969614553746213463024711630256984884134207768538734419216153365573197681917952 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 y #s(literal 1/2 binary64))) (.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ (* x x) (* y y)) (* z z)) (*.f64 x x)))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 z y) z))) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal 499999999999999988998191202828830087182411944733900540386126622484631969614553746213463024711630256984884134207768538734419216153365573197681917952 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ (* x x) (* y y)) (* z z)) (*.f64 x x)))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64))) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 y #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal -4230758200257591/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 z y) z))) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 #s(literal 1/2 binary64) y)))
#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 y #s(literal 1/2 binary64)))
#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 #s(literal 1/2 binary64) y))

soundness1.1s (14.4%)

Memory

6.3MiB live, 613.4MiB allocated

Rules

7 488×	`lower-fma.f64`
7 488×	`lower-fma.f32`
5 374×	`lower-/.f32`
5 360×	`lower-/.f64`
4 980×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	438	6168
1	1460	5526
2	6137	5290
0	8365	5014
0	30	167
0	46	167
1	173	163
2	1433	163
0	8496	163
0	71	1170
1	196	1170
2	566	1168
3	2183	1028
4	6030	1004
0	8152	918
0	39	221
0	57	221
1	213	221
2	1616	221
0	8330	213

Stop Event

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

Compiler

Compiled 448 to 175 computations (60.9% saved)

preprocess188.0ms (2.4%)

Memory

-12.3MiB live, 260.2MiB allocated

Remove

(abs x)

(abs z)

Compiler

Compiled 1 228 to 480 computations (60.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze42.0ms (0.5%)

sample927.0ms (11.9%)

explain130.0ms (1.7%)

preprocess504.0ms (6.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify161.0ms (2.1%)

localize197.0ms (2.5%)

series37.0ms (0.5%)

simplify153.0ms (2%)

rewrite196.0ms (2.5%)

eval94.0ms (1.2%)

prune186.0ms (2.4%)

simplify182.0ms (2.3%)

localize80.0ms (1%)

series65.0ms (0.8%)

simplify138.0ms (1.8%)

rewrite266.0ms (3.4%)

eval250.0ms (3.2%)

prune293.0ms (3.7%)

simplify157.0ms (2%)

localize143.0ms (1.8%)

series62.0ms (0.8%)

simplify151.0ms (1.9%)

rewrite334.0ms (4.3%)

eval196.0ms (2.5%)

prune181.0ms (2.3%)

simplify170.0ms (2.2%)

localize125.0ms (1.6%)

series68.0ms (0.9%)

simplify210.0ms (2.7%)

rewrite232.0ms (3%)

eval245.0ms (3.1%)

prune229.0ms (2.9%)

regimes40.0ms (0.5%)

regimes5.0ms (0.1%)

regimes3.0ms (0%)

regimes16.0ms (0.2%)

regimes4.0ms (0.1%)

regimes2.0ms (0%)

regimes8.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch6.0ms (0.1%)

simplify10.0ms (0.1%)

soundness1.1s (14.4%)

preprocess188.0ms (2.4%)

end0.0ms (0%)

Profiling