Metrics for FRP.Yampa.Vector3:vector3Rho from Yampa-0.10.2

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
100%	99.9%	0%	0.1%	0%	0%	0%	4

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample853.0ms (17.5%)

Memory

38.9MiB live, 1 361.2MiB allocated

Samples

521.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 325.0ms

ival-mult: 187.0ms (57.6% of total)

ival-add: 67.0ms (20.6% of total)

ival-sqrt: 62.0ms (19.1% of total)

ival-true: 6.0ms (1.8% of total)

ival-assert: 3.0ms (0.9% of total)

Bogosity

explain165.0ms (3.4%)

Memory

4.0MiB live, 212.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
163	-	-	`(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))`
0	-	-	`z`
0	-	-	`(*.f64 x x)`
0	-	-	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
0	-	-	`(+.f64 (.f64 x x) (.f64 y y))`
0	-	-	`(*.f64 z z)`
0	-	-	`y`
0	-	-	`(*.f64 y y)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))`	oflow-rescue	162	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	162
↳	`(*.f64 y y)`	overflow	75
↳	`(*.f64 x x)`	overflow	66
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	125
↳	`(*.f64 z z)`	overflow	77
`sqrt.f64`	`(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))`	uflow-rescue	1	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	underflow	1
↳	`(*.f64 y y)`	underflow	51
↳	`(*.f64 x x)`	underflow	58
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	6
↳	`(*.f64 z z)`	underflow	66

Confusion

	Predicted +	Predicted -
+	163	0
-	0	93

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	163	0	0
-	0	0	93

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	93
1	163

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms

512×

valid

Compiler

Compiled 142 to 40 computations (71.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-mult: 13.0ms (60.6% of total)

ival-add: 4.0ms (18.6% of total)

ival-sqrt: 4.0ms (18.6% of total)

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

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

preprocess28.0ms (0.6%)

Memory

-18.8MiB live, 57.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	111
1	69	111
2	148	111
3	291	111
4	468	111
5	520	111
6	522	111
0	9	12
0	15	12
1	19	12
2	26	12
3	28	12
0	28	10

Stop Event

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

Calls

Call 1

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

Outputs
(sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x))))

Symmetry

(abs z)

(abs y)

(abs x)

(sort x y z)

Compiler

Compiled 12 to 9 computations (25% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	41.1%	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

Compiler

Compiled 12 to 9 computations (25% saved)

simplify3.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	42
0	15	42
1	19	42
2	26	42
3	28	42
0	28	37

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
(sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x))))
(fma.f64 z z (fma.f64 y y (*.f64 x x)))
(fma.f64 y y (*.f64 x x))
(*.f64 x x)
x
(*.f64 y y)
y
(*.f64 z z)
z

localize23.0ms (0.5%)

Memory

20.6MiB live, 20.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
accuracy	37.67406234825523	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

Samples

16.0ms

256×

valid

Compiler

Compiled 86 to 20 computations (76.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 5.0ms (57% of total)

ival-add: 2.0ms (22.8% of total)

ival-sqrt: 2.0ms (22.8% of total)

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

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

series52.0ms (1.1%)

Memory

-21.8MiB live, 16.2MiB allocated

Counts

5 → 120

Calls

Call 1

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

Outputs
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf z) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf z) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf z) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf z) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf z) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf z) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf z) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf z) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf z) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf z) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf z) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf z) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf z) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf z) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf z) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf z) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
39.0ms	y	@	0	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* x x) (* y y))
2.0ms	y	@	inf	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* x x) (* y y))
1.0ms	x	@	0	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* x x) (* y y))
1.0ms	z	@	0	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* x x) (* y y))
1.0ms	z	@	inf	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* x x) (* y y))

simplify186.0ms (3.8%)

Memory

35.9MiB live, 183.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	183	1644
1	506	1644
2	1774	1641
3	4772	1539
0	8067	1308

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 117

Calls

Call 1

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

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

rewrite182.0ms (3.7%)

Memory

-15.2MiB live, 238.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
0	15	36
1	50	36
2	407	36
3	5849	36
0	8148	31

Stop Event

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

Counts

5 → 227

Calls

Call 1

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

Outputs
#<batchref>
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eval42.0ms (0.9%)

Memory: 7.3MiB live, 82.2MiB allocated
Compiler: Compiled 9 485 to 1 058 computations (88.8% saved)

prune14.0ms (0.3%)

Memory

-17.2MiB live, 28.6MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	338	6	344
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	339	6	345

Accuracy

100.0%

Counts

345 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	41.1%	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))))
▶	40.4%	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
▶	5.6%	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 y y)))
	81.8%	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (fma.f64 (/.f64 (fma.f64 y y (*.f64 x x)) z) #s(literal 1/2 binary64) z))
▶	100.0%	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))
▶	1.6%	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (neg.f64 x))

Compiler

Compiled 212 to 142 computations (33% saved)

simplify6.0ms (0.1%)

Memory

6.4MiB live, 6.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 y y)
cost-diff	0	(fma.f64 z z (*.f64 y y))
cost-diff	0	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y)))
cost-diff	0	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))))
cost-diff	0	(*.f64 z z)
cost-diff	0	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
cost-diff	0	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 y y))
cost-diff	0	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 y y)))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (neg.f64 x))
cost-diff	0	(hypot.f64 z y)
cost-diff	0	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	157
0	31	149
1	40	149
2	48	149
3	51	149
4	53	149
5	57	149
6	66	149
7	78	149
8	92	149
0	92	141

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))
(hypot.f64 z y)
z
y
#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (neg.f64 x))
(neg.f64 x)
x
(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 y y)))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 y y))
(*.f64 y y)
y
(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
(*.f64 z z)
z
(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y)))
(fma.f64 z z (*.f64 y y))
z
(*.f64 y y)
y

Outputs
#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))
(hypot.f64 z y)
z
y
#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (neg.f64 x))
(neg.f64 x)
x
(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 y y)))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 y y))
(*.f64 y y)
y
(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
(*.f64 z z)
z
(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y)))
(fma.f64 z z (*.f64 y y))
z
(*.f64 y y)
y

localize65.0ms (1.3%)

Memory

-1.2MiB live, 37.5MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 z z (*.f64 y y))
accuracy	0	(*.f64 y y)
accuracy	0	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y)))
accuracy	37.67406234825523	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))))
accuracy	0	(*.f64 z z)
accuracy	0.4785272429954076	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
accuracy	37.67406234825523	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
accuracy	0	(*.f64 y y)
accuracy	37.67406234825523	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 y y)))
accuracy	49.052512313744174	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 y y))
accuracy	0	(neg.f64 x)
accuracy	62.950778678921296	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (neg.f64 x))
accuracy	0	(hypot.f64 z y)
accuracy	0	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))

Samples

27.0ms

256×

valid

Compiler

Compiled 285 to 36 computations (87.4% saved)

Precisions

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

ival-mult: 5.0ms (32.3% of total)

ival-add: 4.0ms (25.8% of total)

ival-hypot: 4.0ms (25.8% of total)

ival-sqrt: 2.0ms (12.9% of total)

ival-neg: 1.0ms (6.5% of total)

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

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

series29.0ms (0.6%)

Memory

-5.1MiB live, 32.5MiB allocated

Counts

13 → 372

Calls

Call 1

Inputs
#s(alt #<batchref> (patch #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (hypot.f64 z y) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (neg.f64 x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 y y))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 y y)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 z z) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 z z (*.f64 y y)) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch (hypot.f64 z y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch (hypot.f64 z y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch (hypot.f64 z y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch (hypot.f64 z y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 z) (#s(alt #<batchref> (patch #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (neg.f64 x)) #<representation binary64>) () ())) ())
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Calls

9 calls:

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

simplify267.0ms (5.5%)

Memory

16.8MiB live, 201.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	260	7352
1	742	7352
2	2599	7335
3	6701	7089
0	8243	6058

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 353

Calls

Call 1

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

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

rewrite245.0ms (5%)

Memory

-67.0MiB live, 218.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	147
0	31	139
1	83	139
2	558	139
3	7500	139
0	8120	131

Stop Event

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

Counts

13 → 161

Calls

Call 1

Inputs
#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))
(hypot.f64 z y)
#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (neg.f64 x))
(neg.f64 x)
(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 y y)))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 y y))
(*.f64 y y)
(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
(*.f64 z z)
(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y)))
(fma.f64 z z (*.f64 y y))

Outputs
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eval65.0ms (1.3%)

Memory: 8.6MiB live, 160.7MiB allocated
Compiler: Compiled 16 231 to 902 computations (94.4% saved)

prune22.0ms (0.4%)

Memory

25.4MiB live, 61.5MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	531	1	532
Fresh	1	0	1
Picked	0	5	5
Done	0	0	0
Total	532	6	538

Accuracy

100.0%

Counts

538 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	41.1%	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))))
✓	40.4%	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
✓	5.6%	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 y y)))
✓	100.0%	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))
✓	1.6%	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (neg.f64 x))
▶	81.8%	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) #s(approx (sqrt (+ (* z z) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) z) (*.f64 y y) z)))

Compiler

Compiled 112 to 73 computations (34.8% saved)

simplify5.0ms (0.1%)

Memory

9.0MiB live, 9.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	64
0	21	64
1	32	64
2	48	64
3	59	64
4	64	64
0	64	52

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize80.0ms (1.6%)

Memory

-16.4MiB live, 103.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) #s(approx (sqrt (+ (* z z) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) z) (*.f64 y y) z)))
accuracy	0.6229698710266077	#s(approx (sqrt (+ (* z z) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) z) (*.f64 y y) z))
accuracy	11.436847349539232	(fma.f64 (/.f64 #s(literal 1/2 binary64) z) (*.f64 y y) z)

Samples

72.0ms

256×

valid

Compiler

Compiled 104 to 33 computations (68.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-div: 31.0ms (50.1% of total)

ival-hypot: 19.0ms (30.7% of total)

ival-mult: 6.0ms (9.7% of total)

ival-add: 3.0ms (4.9% of total)

ival-sqrt: 2.0ms (3.2% of total)

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

exact: 0.0ms (0% of total)

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

series12.0ms (0.3%)

Memory

-6.5MiB live, 31.3MiB allocated

Counts

5 → 108

Calls

Call 1

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

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

Calls

9 calls:

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

simplify281.0ms (5.8%)

Memory

-5.5MiB live, 315.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	254	1724
1	704	1724
2	2460	1719
3	6136	1677
0	8136	1460

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 98

Calls

Call 1

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

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

rewrite191.0ms (3.9%)

Memory

15.7MiB live, 173.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	61
0	21	61
1	91	61
2	733	61
0	8439	49

Stop Event

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

Counts

5 → 85

Calls

Call 1

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

Outputs
#<batchref>
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eval28.0ms (0.6%)

Memory: 6.3MiB live, 40.9MiB allocated
Compiler: Compiled 7 404 to 703 computations (90.5% saved)

prune8.0ms (0.2%)

Memory

19.6MiB live, 19.6MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	183	6	189

Accuracy

100.0%

Counts

189 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	41.1%	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))))
✓	40.4%	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
✓	5.6%	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 y y)))
✓	100.0%	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))
✓	1.6%	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (neg.f64 x))
▶	99.0%	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) #s(approx (sqrt (+ (* z z) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) z) y) y z)))

Compiler

Compiled 112 to 73 computations (34.8% saved)

simplify4.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	66
0	21	66
1	32	66
2	49	66
3	57	66
4	62	66
0	62	54

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize183.0ms (3.8%)

Memory

-21.3MiB live, 63.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1/2 binary64) z)
accuracy	0	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) #s(approx (sqrt (+ (* z z) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) z) y) y z)))
accuracy	0.2421875	(*.f64 (/.f64 #s(literal 1/2 binary64) z) y)
accuracy	0.6229698710266077	#s(approx (sqrt (+ (* z z) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) z) y) y z))

Samples

99.0ms

256×

valid

Compiler

Compiled 108 to 34 computations (68.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 91.0ms

ival-hypot: 58.0ms (63.9% of total)

ival-add: 21.0ms (23.1% of total)

ival-mult: 7.0ms (7.7% of total)

ival-div: 2.0ms (2.2% of total)

ival-sqrt: 2.0ms (2.2% of total)

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

exact: 0.0ms (0% of total)

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

series11.0ms (0.2%)

Memory

15.2MiB live, 15.2MiB allocated

Counts

5 → 120

Calls

Call 1

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

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

9 calls:

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

simplify524.0ms (10.8%)

Memory

-24.8MiB live, 302.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	256	1808
1	709	1808
2	2469	1803
3	6160	1761
0	8153	1544

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 110

Calls

Call 1

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

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

rewrite165.0ms (3.4%)

Memory

4.4MiB live, 269.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	63
0	21	63
1	91	63
2	724	63
0	8607	51

Stop Event

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

Counts

5 → 109

Calls

Call 1

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

Outputs
#<batchref>
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eval29.0ms (0.6%)

Memory: 2.6MiB live, 118.6MiB allocated
Compiler: Compiled 8 683 to 819 computations (90.6% saved)

prune47.0ms (1%)

Memory

-4.7MiB live, 61.6MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	219	6	225

Accuracy

100.0%

Counts

225 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	41.1%	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))))
✓	40.4%	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
✓	5.6%	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 y y)))
✓	100.0%	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))
✓	1.6%	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (neg.f64 x))
✓	99.0%	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) #s(approx (sqrt (+ (* z z) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) z) y) y z)))

Compiler

Compiled 290 to 114 computations (60.7% saved)

regimes37.0ms (0.8%)

Memory

10.3MiB live, 88.7MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

9 calls:

8.0ms	(*.f64 y y)
4.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
4.0ms	y
4.0ms	x
4.0ms	z

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`z`
100.0%	1	`(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))`
100.0%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
100.0%	1	`(+.f64 (.f64 x x) (.f64 y y))`
100.0%	1	`(*.f64 x x)`
100.0%	1	`(*.f64 y y)`
100.0%	1	`(*.f64 z z)`

Compiler

Compiled 42 to 44 computations (-4.8% saved)

regimes97.0ms (2%)

Memory

-20.4MiB live, 60.3MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

9 calls:

39.0ms	(*.f64 z z)
34.0ms	y
3.0ms	z
3.0ms	x
3.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`y`
99.0%	1	`z`
99.0%	1	`(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))`
99.0%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
99.0%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.0%	1	`(*.f64 x x)`
99.0%	1	`(*.f64 y y)`
99.0%	1	`(*.f64 z z)`

Compiler

Compiled 42 to 44 computations (-4.8% saved)

regimes99.0ms (2%)

Memory

9.6MiB live, 47.6MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

9 calls:

81.0ms	(+.f64 (.f64 x x) (.f64 y y))
2.0ms	z
2.0ms	x
2.0ms	y
2.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
41.1%	1	`y`
41.1%	1	`z`
41.1%	1	`x`
41.1%	1	`(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))`
41.1%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
41.1%	1	`(+.f64 (.f64 x x) (.f64 y y))`
41.1%	1	`(*.f64 x x)`
41.1%	1	`(*.f64 y y)`
41.1%	1	`(*.f64 z z)`

Compiler

Compiled 42 to 44 computations (-4.8% saved)

regimes91.0ms (1.9%)

Memory

9.9MiB live, 47.9MiB allocated

Counts

3 → 1

Calls

Call 1

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

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

Calls

9 calls:

75.0ms	(*.f64 x x)
2.0ms	z
2.0ms	x
2.0ms	y
2.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
40.4%	1	`x`
40.4%	1	`y`
40.4%	1	`(+.f64 (.f64 x x) (.f64 y y))`
40.4%	1	`(*.f64 y y)`
40.4%	1	`z`
40.4%	1	`(*.f64 x x)`
40.4%	1	`(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))`
40.4%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
40.4%	1	`(*.f64 z z)`

Compiler

Compiled 42 to 44 computations (-4.8% saved)

regimes19.0ms (0.4%)

Memory

-32.1MiB live, 49.1MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

9 calls:

4.0ms	x
3.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
2.0ms	z
2.0ms	y
2.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
5.6%	1	`x`
5.6%	1	`(*.f64 x x)`
5.6%	1	`y`
5.6%	1	`(+.f64 (.f64 x x) (.f64 y y))`
5.6%	1	`(*.f64 y y)`
5.6%	1	`z`
5.6%	1	`(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))`
5.6%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
5.6%	1	`(*.f64 z z)`

Compiler

Compiled 42 to 44 computations (-4.8% saved)

regimes12.0ms (0.2%)

Memory

24.4MiB live, 24.4MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

9 calls:

1.0ms	y
1.0ms	z
1.0ms	x
1.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
1.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
1.6%	1	`(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))`
1.6%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
1.6%	1	`(*.f64 z z)`
1.6%	1	`z`
1.6%	1	`x`
1.6%	1	`(+.f64 (.f64 x x) (.f64 y y))`
1.6%	1	`(*.f64 y y)`
1.6%	1	`y`
1.6%	1	`(*.f64 x x)`

Compiler

Compiled 42 to 44 computations (-4.8% saved)

simplify31.0ms (0.6%)

Memory

-15.6MiB live, 62.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	112
1	35	112
2	37	112
3	38	112

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness588.0ms (12.1%)

Memory

14.9MiB live, 519.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	260	7352
1	742	7352
2	2599	7335
3	6701	7089
0	8243	6058
0	17	61
0	21	61
1	91	61
2	733	61
0	8439	49
0	183	1644
1	506	1644
2	1774	1641
3	4772	1539
0	8067	1308

Stop Event

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

Compiler

Compiled 165 to 78 computations (52.7% saved)

preprocess72.0ms (1.5%)

Memory: 10.3MiB live, 174.3MiB allocated
Compiler: Compiled 422 to 198 computations (53.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	33	111
1	69	111
2	148	111
3	291	111
4	468	111
5	520	111
6	522	111
0	9	12
0	15	12
1	19	12
2	26	12
3	28	12
0	28	10

Iter	Nodes	Cost
0	22	157
0	31	149
1	40	149
2	48	149
3	51	149
4	53	149
5	57	149
6	66	149
7	78	149
8	92	149
0	92	141

Iter	Nodes	Cost
0	33	111
1	69	111
2	148	111
3	291	111
4	468	111
5	520	111
6	522	111
0	9	12
0	15	12
1	19	12
2	26	12
3	28	12
0	28	10

Iter	Nodes	Cost
0	22	157
0	31	149
1	40	149
2	48	149
3	51	149
4	53	149
5	57	149
6	66	149
7	78	149
8	92	149
0	92	141

start0.0ms (0%)

analyze1.0ms (0%)

sample853.0ms (17.5%)

explain165.0ms (3.4%)

preprocess28.0ms (0.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize23.0ms (0.5%)

series52.0ms (1.1%)

simplify186.0ms (3.8%)

rewrite182.0ms (3.7%)

eval42.0ms (0.9%)

prune14.0ms (0.3%)

simplify6.0ms (0.1%)

localize65.0ms (1.3%)

series29.0ms (0.6%)

simplify267.0ms (5.5%)

rewrite245.0ms (5%)

eval65.0ms (1.3%)

prune22.0ms (0.4%)

simplify5.0ms (0.1%)

localize80.0ms (1.6%)

series12.0ms (0.3%)

simplify281.0ms (5.8%)

rewrite191.0ms (3.9%)

eval28.0ms (0.6%)

prune8.0ms (0.2%)

simplify4.0ms (0.1%)

localize183.0ms (3.8%)

series11.0ms (0.2%)

simplify524.0ms (10.8%)

rewrite165.0ms (3.4%)

eval29.0ms (0.6%)

prune47.0ms (1%)

regimes37.0ms (0.8%)

regimes97.0ms (2%)

regimes99.0ms (2%)

regimes91.0ms (1.9%)

regimes19.0ms (0.4%)

regimes12.0ms (0.2%)

simplify31.0ms (0.6%)

soundness588.0ms (12.1%)

preprocess72.0ms (1.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	33	111
1	69	111
2	148	111
3	291	111
4	468	111
5	520	111
6	522	111
0	9	12
0	15	12
1	19	12
2	26	12
3	28	12
0	28	10

Iter	Nodes	Cost
0	22	157
0	31	149
1	40	149
2	48	149
3	51	149
4	53	149
5	57	149
6	66	149
7	78	149
8	92	149
0	92	141