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

analyze2.0ms (0.1%)

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 16 to 10 computations (37.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

const: 0.0ms (0% of total)

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

sample1.5s (50.8%)

Results

1.2s

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 384.0ms

ival-mult: 211.0ms (54.9% of total)

ival-add: 90.0ms (23.4% of total)

ival-sqrt: 72.0ms (18.7% of total)

const: 8.0ms (2.1% of total)

backward-pass: 4.0ms (1% of total)

Bogosity

preprocess63.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

212×	`fma-neg`
117×	`fma-define`
45×	`unsub-neg`
31×	`neg-sub0`
30×	`sub-neg`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	551
1	84	507
2	176	507
3	391	507
4	675	507
5	825	507
6	841	507

Stop Event

1×

saturated

Calls

Call 1

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

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

Symmetry

(abs x)

(abs y)

(abs z)

(sort x y z)

explain101.0ms (3.3%)

FPErrors

Click to see full error table

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

Results

65.0ms

512×

256

valid

Compiler

Compiled 107 to 29 computations (72.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 11.0ms (50.2% of total)

ival-add: 5.0ms (22.8% of total)

ival-sqrt: 5.0ms (22.8% of total)

const: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 13 to 7 computations (46.2% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	45.1%	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

Compiler

Compiled 15 to 9 computations (40% saved)

localize46.0ms (1.5%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	100.0%	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
✓	45.1%	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

Results

34.0ms

256×

256

valid

Compiler

Compiled 46 to 10 computations (78.3% saved)

Precisions

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

ival-mult: 5.0ms (49.9% of total)

ival-add: 3.0ms (29.9% of total)

ival-sqrt: 2.0ms (20% of total)

const: 0.0ms (0% of total)

series13.0ms (0.4%)

Counts

2 → 72

Calls

Call 1

Inputs
#<alt (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))>
#<alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))>

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

Calls

18 calls:

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

rewrite444.0ms (14.7%)

Algorithm

1×	batch-egg-rewrite

Rules

971×	`log1p-expm1-u`
971×	`expm1-log1p-u`
487×	`fma-define`
437×	`log-prod`
229×	`fma-neg`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	82
1	208	50
2	2762	50

Stop Event

1×	node limit

Counts

2 → 138

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))

Outputs
(+.f64 #s(literal 0 binary64) (hypot.f64 x (hypot.f64 y z)))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (hypot.f64 y z)))) (cbrt.f64 (exp.f64 (hypot.f64 x (hypot.f64 y z)))))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (hypot.f64 y z))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x (hypot.f64 y z))))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x (hypot.f64 y z))))))
(-.f64 (exp.f64 (log1p.f64 (hypot.f64 x (hypot.f64 y z)))) #s(literal 1 binary64))
(*.f64 (hypot.f64 x (hypot.f64 y z)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (hypot.f64 x (hypot.f64 y z)))
(.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z))) (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z)))))
(.f64 (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z)))) (cbrt.f64 (hypot.f64 x (hypot.f64 y z))))
(.f64 (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (hypot.f64 x (hypot.f64 y z)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z)))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z)))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (.f64 z z)))) (sqrt.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
(/.f64 (hypot.f64 (.f64 z (.f64 z z)) (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) #s(literal 3/2 binary64))) (hypot.f64 (+.f64 (.f64 x x) (.f64 y y)) (sqrt.f64 (.f64 (.f64 z z) (-.f64 (.f64 z z) (+.f64 (.f64 x x) (*.f64 y y)))))))
(pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))) #s(literal 1/2 binary64))
(pow.f64 (hypot.f64 x (hypot.f64 y z)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))
(fabs.f64 (hypot.f64 x (hypot.f64 y z)))
(log.f64 (exp.f64 (hypot.f64 x (hypot.f64 y z))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (hypot.f64 x (hypot.f64 y z)))))
(cbrt.f64 (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (hypot.f64 x (hypot.f64 y z))))
(hypot.f64 x (hypot.f64 y z))
(hypot.f64 z (hypot.f64 x y))
(hypot.f64 (hypot.f64 x y) z)
(hypot.f64 (hypot.f64 y z) x)
(log1p.f64 (expm1.f64 (hypot.f64 x (hypot.f64 y z))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z))))))
(exp.f64 (.f64 (log.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z)))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))) #s(literal 1 binary64)))
(+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))
(+.f64 (.f64 x x) (.f64 (+.f64 (.f64 y y) (.f64 z z)) #s(literal 1 binary64)))
(+.f64 (.f64 y y) (+.f64 (.f64 x x) (*.f64 z z)))
(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
(+.f64 (.f64 z z) (+.f64 (.f64 x x) (*.f64 y y)))
(+.f64 (+.f64 (.f64 y y) (.f64 z z)) (*.f64 x x))
(+.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))
(+.f64 (+.f64 (.f64 z z) (.f64 x x)) (*.f64 y y))
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z))))) (cbrt.f64 (exp.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z))))))) (log.f64 (cbrt.f64 (exp.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z)))))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z)))))))
(-.f64 (exp.f64 (log1p.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))) #s(literal 1 binary64))
(-.f64 (/.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (/.f64 (.f64 (.f64 z z) (.f64 z z)) (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))
(.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z))) #s(literal 1 binary64))
(*.f64 (hypot.f64 x (hypot.f64 y z)) (hypot.f64 x (hypot.f64 y z)))
(.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z))))
(.f64 (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z)))) (pow.f64 (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))) #s(literal 2 binary64)))
(.f64 (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z)))) (*.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z))) (hypot.f64 x (hypot.f64 y z))))
(.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z)))) #s(literal 2 binary64)) (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))))
(.f64 (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z))) #s(literal 1/4 binary64)) (.f64 (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z))) #s(literal 1/4 binary64)) (hypot.f64 x (hypot.f64 y z))))
(.f64 (fma.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (.f64 (.f64 z z) (.f64 z z)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (-.f64 (.f64 z z) (+.f64 (.f64 x x) (*.f64 y y)))))))
(.f64 (-.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (.f64 z z))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))
(.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z))) #s(literal 1/4 binary64))) (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z))) #s(literal 1/4 binary64)))
(.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))) (cbrt.f64 (hypot.f64 x (hypot.f64 y z))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (-.f64 (.f64 z z) (+.f64 (.f64 x x) (.f64 y y))))) (fma.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (.f64 (.f64 z z) (.f64 z z))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (-.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (*.f64 z z)))))
(/.f64 (fma.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (.f64 (.f64 z z) (.f64 z z)))) (+.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (-.f64 (.f64 z z) (+.f64 (.f64 x x) (.f64 y y))))))
(/.f64 (fma.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (.f64 (.f64 z z) (.f64 z z)))) (+.f64 (.f64 (.f64 z z) (.f64 z z)) (-.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))))
(/.f64 (-.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (.f64 z z))) (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
(/.f64 (neg.f64 (fma.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (.f64 (.f64 z z) (.f64 z z))))) (neg.f64 (+.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (-.f64 (.f64 z z) (+.f64 (.f64 x x) (.f64 y y)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (.f64 z z)))) (neg.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
(/.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (pow.f64 (+.f64 (.f64 y y) (.f64 z z)) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (.f64 (+.f64 (.f64 y y) (.f64 z z)) (+.f64 (.f64 y y) (.f64 z z))) (.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (+.f64 (.f64 y y) (.f64 z z)) (+.f64 (.f64 y y) (.f64 z z)))) (-.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))
(/.f64 (-.f64 (.f64 (.f64 z z) (.f64 z z)) (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))) (-.f64 (.f64 z z) (+.f64 (.f64 x x) (*.f64 y y))))
(pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))) #s(literal 1 binary64))
(pow.f64 (hypot.f64 x (hypot.f64 y z)) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))) #s(literal 3 binary64))
(pow.f64 (/.f64 (.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z))) (-.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (.f64 z z)))) (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (/.f64 (.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z))) (-.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (.f64 z z)))) (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
(log.f64 (exp.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))))
(log.f64 (.f64 (exp.f64 (.f64 x x)) (.f64 (exp.f64 (.f64 y y)) (exp.f64 (*.f64 z z)))))
(log.f64 (.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 x x))) (.f64 (exp.f64 (.f64 y y)) (exp.f64 (*.f64 z z)))))
(log.f64 (.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 x x))) (exp.f64 (+.f64 (.f64 y y) (.f64 z z)))))
(log.f64 (.f64 (exp.f64 (+.f64 (.f64 x x) (.f64 y y))) (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 z z)))))
(log.f64 (.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 (.f64 x x) (.f64 y y)))) (exp.f64 (.f64 z z))))
(log.f64 (.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 (.f64 x x) (.f64 y y)))) (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 z z)))))
(log.f64 (.f64 (exp.f64 (.f64 z z)) (+.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 (.f64 x x) (.f64 y y))))))
(log.f64 (.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 z z))) (exp.f64 (+.f64 (.f64 x x) (.f64 y y)))))
(log.f64 (.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 z z))) (+.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 (.f64 x x) (.f64 y y))))))
(log.f64 (.f64 (.f64 (exp.f64 (.f64 y y)) (exp.f64 (.f64 z z))) (exp.f64 (*.f64 x x))))
(log.f64 (.f64 (.f64 (exp.f64 (.f64 y y)) (exp.f64 (.f64 z z))) (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 x x)))))
(log.f64 (.f64 (exp.f64 (+.f64 (.f64 y y) (.f64 z z))) (exp.f64 (.f64 x x))))
(log.f64 (.f64 (exp.f64 (+.f64 (.f64 y y) (.f64 z z))) (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 x x)))))
(cbrt.f64 (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))))
(log1p.f64 (expm1.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))))
(exp.f64 (log.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))))
(exp.f64 (.f64 (log.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z)))) #s(literal 1 binary64)))
(fma.f64 x x (+.f64 (.f64 y y) (.f64 z z)))
(fma.f64 x x (.f64 (+.f64 (.f64 y y) (*.f64 z z)) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (+.f64 (.f64 y y) (*.f64 z z)))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 z z)) #s(literal 1 binary64)))
(fma.f64 y y (+.f64 (.f64 x x) (.f64 z z)))
(fma.f64 (.f64 y y) #s(literal 1 binary64) (+.f64 (.f64 x x) (*.f64 z z)))
(fma.f64 (+.f64 (.f64 x x) (.f64 y y)) #s(literal 1 binary64) (*.f64 z z))
(fma.f64 z z (+.f64 (.f64 x x) (.f64 y y)))
(fma.f64 (.f64 z z) #s(literal 1 binary64) (+.f64 (.f64 x x) (*.f64 y y)))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 (+.f64 (.f64 y y) (.f64 z z)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 y y) (+.f64 (.f64 x x) (*.f64 z z)))
(fma.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
(fma.f64 #s(literal 1 binary64) (.f64 z z) (+.f64 (.f64 x x) (*.f64 y y)))
(fma.f64 #s(literal 1 binary64) (+.f64 (.f64 y y) (.f64 z z)) (*.f64 x x))
(fma.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))) (.f64 z z))
(fma.f64 (cbrt.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (.f64 z z))
(fma.f64 (cbrt.f64 (.f64 z z)) (cbrt.f64 (.f64 (.f64 z z) (.f64 z z))) (+.f64 (.f64 x x) (.f64 y y)))
(fma.f64 (cbrt.f64 (.f64 z z)) (.f64 (cbrt.f64 z) z) (+.f64 (.f64 x x) (.f64 y y)))
(fma.f64 (cbrt.f64 (.f64 (.f64 z z) (.f64 z z))) (cbrt.f64 (.f64 z z)) (+.f64 (.f64 x x) (.f64 y y)))
(fma.f64 (cbrt.f64 (.f64 y y)) (cbrt.f64 (.f64 (.f64 y y) (.f64 y y))) (+.f64 (.f64 x x) (.f64 z z)))
(fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) y) (+.f64 (.f64 x x) (.f64 z z)))
(fma.f64 (cbrt.f64 (.f64 (.f64 y y) (.f64 y y))) (cbrt.f64 (.f64 y y)) (+.f64 (.f64 x x) (.f64 z z)))
(fma.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 (.f64 (.f64 x x) (.f64 x x))) (+.f64 (.f64 y y) (.f64 z z)))
(fma.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (.f64 y y) (*.f64 z z)) #s(literal 1 binary64)))
(fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) x) (+.f64 (.f64 y y) (.f64 z z)))
(fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) x) (.f64 (+.f64 (.f64 y y) (*.f64 z z)) #s(literal 1 binary64)))
(fma.f64 (cbrt.f64 (.f64 (.f64 x x) (.f64 x x))) (cbrt.f64 (.f64 x x)) (+.f64 (.f64 y y) (.f64 z z)))
(fma.f64 (cbrt.f64 (.f64 (.f64 x x) (.f64 x x))) (cbrt.f64 (.f64 x x)) (.f64 (+.f64 (.f64 y y) (*.f64 z z)) #s(literal 1 binary64)))
(fma.f64 (hypot.f64 x y) (hypot.f64 x y) (*.f64 z z))
(fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (.f64 (pow.f64 y #s(literal 1/2 binary64)) y) (+.f64 (.f64 x x) (*.f64 z z)))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (.f64 (pow.f64 x #s(literal 1/2 binary64)) x) (+.f64 (.f64 y y) (*.f64 z z)))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (.f64 (pow.f64 x #s(literal 1/2 binary64)) x) (.f64 (+.f64 (.f64 y y) (.f64 z z)) #s(literal 1 binary64)))
(fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) z) (+.f64 (.f64 x x) (*.f64 y y)))
(fma.f64 (.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x x)))) (+.f64 (.f64 x x) (.f64 y y))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x x))))) (.f64 z z))
(fma.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 y y) (.f64 y y))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) (.f64 y y))) (*.f64 z z))
(fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 y y) (.f64 z z))) (cbrt.f64 (+.f64 (.f64 y y) (.f64 z z)))) (cbrt.f64 (+.f64 (.f64 y y) (.f64 z z))) (.f64 x x))
(fma.f64 (.f64 y (pow.f64 y #s(literal 1/2 binary64))) (pow.f64 y #s(literal 1/2 binary64)) (+.f64 (.f64 x x) (*.f64 z z)))
(fma.f64 (.f64 z (sqrt.f64 z)) (sqrt.f64 z) (+.f64 (.f64 x x) (*.f64 y y)))
(fma.f64 (.f64 x (pow.f64 x #s(literal 1/2 binary64))) (pow.f64 x #s(literal 1/2 binary64)) (+.f64 (.f64 y y) (*.f64 z z)))
(fma.f64 (.f64 x (pow.f64 x #s(literal 1/2 binary64))) (pow.f64 x #s(literal 1/2 binary64)) (.f64 (+.f64 (.f64 y y) (.f64 z z)) #s(literal 1 binary64)))
(fma.f64 (hypot.f64 y z) (hypot.f64 y z) (*.f64 x x))
(fma.f64 (.f64 x (cbrt.f64 (.f64 x x))) (cbrt.f64 x) (+.f64 (.f64 y y) (.f64 z z)))
(fma.f64 (.f64 x (cbrt.f64 (.f64 x x))) (cbrt.f64 x) (.f64 (+.f64 (.f64 y y) (*.f64 z z)) #s(literal 1 binary64)))
(fma.f64 (.f64 z (cbrt.f64 (.f64 z z))) (cbrt.f64 z) (+.f64 (.f64 x x) (.f64 y y)))
(fma.f64 (.f64 y (cbrt.f64 (.f64 y y))) (cbrt.f64 y) (+.f64 (.f64 x x) (.f64 z z)))

simplify120.0ms (4%)

Algorithm

1×	egg-herbie

Rules

616×	`times-frac`
396×	`associate-+r+`
349×	`associate-+l+`
260×	`distribute-rgt-in`
259×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	485	12262
1	1300	10858
2	4180	10630

Stop Event

1×	node limit

Counts

210 → 248

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))))
(+.f64 (sqrt.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))) (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))))))))
(+.f64 (sqrt.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 3 binary64)))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))))))))
(+.f64 (sqrt.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))))) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 3 binary64))))) (.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 5 binary64)))))))))))
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64))))))
(.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64))))))))
(*.f64 #s(literal -1 binary64) x)
(.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64)))))))
(.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64))))))))
(.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64)))))))))
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))))
(+.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))) (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))))))))
(+.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))) (.f64 (pow.f64 y #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 3 binary64)))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))))))))
(+.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))) (.f64 (pow.f64 y #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))))) (.f64 (pow.f64 y #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 3 binary64))))) (.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 5 binary64)))))))))))
y
(.f64 y (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 y #s(literal 2 binary64))))))
(.f64 y (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 y #s(literal 2 binary64)))))))
(.f64 y (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64)))) (+.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 y #s(literal 2 binary64))))))))
(*.f64 #s(literal -1 binary64) y)
(.f64 #s(literal -1 binary64) (.f64 y (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 y #s(literal 2 binary64)))))))
(.f64 #s(literal -1 binary64) (.f64 y (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 y #s(literal 2 binary64))))))))
(.f64 #s(literal -1 binary64) (.f64 y (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64)))) (+.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 y #s(literal 2 binary64)))))))))
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64))))
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(/.f64 (neg.f64 (fma.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (.f64 (.f64 z z) (.f64 z z))))) (neg.f64 (+.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (-.f64 (.f64 z z) (+.f64 (.f64 x x) (.f64 y y)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (.f64 z z)))) (neg.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
(/.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (pow.f64 (+.f64 (.f64 y y) (.f64 z z)) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (.f64 (+.f64 (.f64 y y) (.f64 z z)) (+.f64 (.f64 y y) (.f64 z z))) (.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (+.f64 (.f64 y y) (.f64 z z)) (+.f64 (.f64 y y) (.f64 z z)))) (-.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))
(/.f64 (-.f64 (.f64 (.f64 z z) (.f64 z z)) (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))) (-.f64 (.f64 z z) (+.f64 (.f64 x x) (*.f64 y y))))
(pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))) #s(literal 1 binary64))
(pow.f64 (hypot.f64 x (hypot.f64 y z)) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))) #s(literal 3 binary64))
(pow.f64 (/.f64 (.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z))) (-.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (.f64 z z)))) (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (/.f64 (.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z))) (-.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (.f64 (.f64 z z) (.f64 z z)))) (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
(log.f64 (exp.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))))
(log.f64 (.f64 (exp.f64 (.f64 x x)) (.f64 (exp.f64 (.f64 y y)) (exp.f64 (*.f64 z z)))))
(log.f64 (.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 x x))) (.f64 (exp.f64 (.f64 y y)) (exp.f64 (*.f64 z z)))))
(log.f64 (.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 x x))) (exp.f64 (+.f64 (.f64 y y) (.f64 z z)))))
(log.f64 (.f64 (exp.f64 (+.f64 (.f64 x x) (.f64 y y))) (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 z z)))))
(log.f64 (.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 (.f64 x x) (.f64 y y)))) (exp.f64 (.f64 z z))))
(log.f64 (.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 (.f64 x x) (.f64 y y)))) (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 z z)))))
(log.f64 (.f64 (exp.f64 (.f64 z z)) (+.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 (.f64 x x) (.f64 y y))))))
(log.f64 (.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 z z))) (exp.f64 (+.f64 (.f64 x x) (.f64 y y)))))
(log.f64 (.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 z z))) (+.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 (.f64 x x) (.f64 y y))))))
(log.f64 (.f64 (.f64 (exp.f64 (.f64 y y)) (exp.f64 (.f64 z z))) (exp.f64 (*.f64 x x))))
(log.f64 (.f64 (.f64 (exp.f64 (.f64 y y)) (exp.f64 (.f64 z z))) (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 x x)))))
(log.f64 (.f64 (exp.f64 (+.f64 (.f64 y y) (.f64 z z))) (exp.f64 (.f64 x x))))
(log.f64 (.f64 (exp.f64 (+.f64 (.f64 y y) (.f64 z z))) (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 x x)))))
(cbrt.f64 (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))))
(log1p.f64 (expm1.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))))
(exp.f64 (log.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))))
(exp.f64 (.f64 (log.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z)))) #s(literal 1 binary64)))
(fma.f64 x x (+.f64 (.f64 y y) (.f64 z z)))
(fma.f64 x x (.f64 (+.f64 (.f64 y y) (*.f64 z z)) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (+.f64 (.f64 y y) (*.f64 z z)))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 z z)) #s(literal 1 binary64)))
(fma.f64 y y (+.f64 (.f64 x x) (.f64 z z)))
(fma.f64 (.f64 y y) #s(literal 1 binary64) (+.f64 (.f64 x x) (*.f64 z z)))
(fma.f64 (+.f64 (.f64 x x) (.f64 y y)) #s(literal 1 binary64) (*.f64 z z))
(fma.f64 z z (+.f64 (.f64 x x) (.f64 y y)))
(fma.f64 (.f64 z z) #s(literal 1 binary64) (+.f64 (.f64 x x) (*.f64 y y)))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 (+.f64 (.f64 y y) (.f64 z z)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 y y) (+.f64 (.f64 x x) (*.f64 z z)))
(fma.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
(fma.f64 #s(literal 1 binary64) (.f64 z z) (+.f64 (.f64 x x) (*.f64 y y)))
(fma.f64 #s(literal 1 binary64) (+.f64 (.f64 y y) (.f64 z z)) (*.f64 x x))
(fma.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))) (.f64 z z))
(fma.f64 (cbrt.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (.f64 z z))
(fma.f64 (cbrt.f64 (.f64 z z)) (cbrt.f64 (.f64 (.f64 z z) (.f64 z z))) (+.f64 (.f64 x x) (.f64 y y)))
(fma.f64 (cbrt.f64 (.f64 z z)) (.f64 (cbrt.f64 z) z) (+.f64 (.f64 x x) (.f64 y y)))
(fma.f64 (cbrt.f64 (.f64 (.f64 z z) (.f64 z z))) (cbrt.f64 (.f64 z z)) (+.f64 (.f64 x x) (.f64 y y)))
(fma.f64 (cbrt.f64 (.f64 y y)) (cbrt.f64 (.f64 (.f64 y y) (.f64 y y))) (+.f64 (.f64 x x) (.f64 z z)))
(fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) y) (+.f64 (.f64 x x) (.f64 z z)))
(fma.f64 (cbrt.f64 (.f64 (.f64 y y) (.f64 y y))) (cbrt.f64 (.f64 y y)) (+.f64 (.f64 x x) (.f64 z z)))
(fma.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 (.f64 (.f64 x x) (.f64 x x))) (+.f64 (.f64 y y) (.f64 z z)))
(fma.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (.f64 y y) (*.f64 z z)) #s(literal 1 binary64)))
(fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) x) (+.f64 (.f64 y y) (.f64 z z)))
(fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) x) (.f64 (+.f64 (.f64 y y) (*.f64 z z)) #s(literal 1 binary64)))
(fma.f64 (cbrt.f64 (.f64 (.f64 x x) (.f64 x x))) (cbrt.f64 (.f64 x x)) (+.f64 (.f64 y y) (.f64 z z)))
(fma.f64 (cbrt.f64 (.f64 (.f64 x x) (.f64 x x))) (cbrt.f64 (.f64 x x)) (.f64 (+.f64 (.f64 y y) (*.f64 z z)) #s(literal 1 binary64)))
(fma.f64 (hypot.f64 x y) (hypot.f64 x y) (*.f64 z z))
(fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (.f64 (pow.f64 y #s(literal 1/2 binary64)) y) (+.f64 (.f64 x x) (*.f64 z z)))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (.f64 (pow.f64 x #s(literal 1/2 binary64)) x) (+.f64 (.f64 y y) (*.f64 z z)))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (.f64 (pow.f64 x #s(literal 1/2 binary64)) x) (.f64 (+.f64 (.f64 y y) (.f64 z z)) #s(literal 1 binary64)))
(fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) z) (+.f64 (.f64 x x) (*.f64 y y)))
(fma.f64 (.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x x)))) (+.f64 (.f64 x x) (.f64 y y))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x x))))) (.f64 z z))
(fma.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 y y) (.f64 y y))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) (.f64 y y))) (*.f64 z z))
(fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 y y) (.f64 z z))) (cbrt.f64 (+.f64 (.f64 y y) (.f64 z z)))) (cbrt.f64 (+.f64 (.f64 y y) (.f64 z z))) (.f64 x x))
(fma.f64 (.f64 y (pow.f64 y #s(literal 1/2 binary64))) (pow.f64 y #s(literal 1/2 binary64)) (+.f64 (.f64 x x) (*.f64 z z)))
(fma.f64 (.f64 z (sqrt.f64 z)) (sqrt.f64 z) (+.f64 (.f64 x x) (*.f64 y y)))
(fma.f64 (.f64 x (pow.f64 x #s(literal 1/2 binary64))) (pow.f64 x #s(literal 1/2 binary64)) (+.f64 (.f64 y y) (*.f64 z z)))
(fma.f64 (.f64 x (pow.f64 x #s(literal 1/2 binary64))) (pow.f64 x #s(literal 1/2 binary64)) (.f64 (+.f64 (.f64 y y) (.f64 z z)) #s(literal 1 binary64)))
(fma.f64 (hypot.f64 y z) (hypot.f64 y z) (*.f64 x x))
(fma.f64 (.f64 x (cbrt.f64 (.f64 x x))) (cbrt.f64 x) (+.f64 (.f64 y y) (.f64 z z)))
(fma.f64 (.f64 x (cbrt.f64 (.f64 x x))) (cbrt.f64 x) (.f64 (+.f64 (.f64 y y) (*.f64 z z)) #s(literal 1 binary64)))
(fma.f64 (.f64 z (cbrt.f64 (.f64 z z))) (cbrt.f64 z) (+.f64 (.f64 x x) (.f64 y y)))
(fma.f64 (.f64 y (cbrt.f64 (.f64 y y))) (cbrt.f64 y) (+.f64 (.f64 x x) (.f64 z z)))

Outputs
(sqrt.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))))
(hypot.f64 y z)
(+.f64 (sqrt.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))) (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 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 y z))
(+.f64 (sqrt.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 3 binary64)))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))))))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 y y)))) (.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64)))) (.f64 x x)))) (.f64 x x) (hypot.f64 y z))
(+.f64 (sqrt.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))))) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 3 binary64))))) (.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 5 binary64)))))))))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 y y)))) (.f64 (fma.f64 #s(literal -1/8 binary64) (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) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 5 binary64)))) (.f64 #s(literal 1/16 binary64) (.f64 x x)))) (.f64 x x))) (*.f64 x x) (hypot.f64 y z))
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 z z (.f64 y y)) (*.f64 x x)) #s(literal 1 binary64)))
(.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64)))))))
(+.f64 x (.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 z z (.f64 y y)) (.f64 x x)) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64))))))))
(.f64 x (+.f64 #s(literal 1 binary64) (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 1/16 binary64) (/.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 z z (.f64 y y)) (.f64 x x)))))))
(*.f64 #s(literal -1 binary64) x)
(neg.f64 x)
(.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64)))))))
(.f64 x (neg.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 z z (.f64 y y)) (*.f64 x x)) #s(literal 1 binary64))))
(.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64))))))))
(-.f64 (neg.f64 x) (.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 z z (.f64 y y)) (.f64 x x)) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64)))))))))
(-.f64 (.f64 x (neg.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 1/16 binary64) (/.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 z z (.f64 y y)) (.f64 x x))))))) x)
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))))
(hypot.f64 z x)
(+.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))) (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))))))))
(fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 x x)))) (*.f64 y y)) (hypot.f64 z x))
(+.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))) (.f64 (pow.f64 y #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64))) #s(literal 3 binary64)))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 z #s(literal 2 binary64)))))))))
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(fma.f64 (.f64 z (cbrt.f64 (.f64 z z))) (cbrt.f64 z) (+.f64 (.f64 x x) (.f64 y y)))
(fma.f64 (cbrt.f64 (.f64 z z)) (.f64 z (cbrt.f64 z)) (fma.f64 y y (*.f64 x x)))
(fma.f64 (.f64 y (cbrt.f64 (.f64 y y))) (cbrt.f64 y) (+.f64 (.f64 x x) (.f64 z z)))
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eval323.0ms (10.7%)

Compiler: Compiled 9857 to 3548 computations (64% saved)

prune40.0ms (1.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	456	2	458
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	457	2	459

Accuracy

100.0%

Counts

459 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 y z)
▶	98.8%	z

Compiler

Compiled 10 to 7 computations (30% saved)

localize31.0ms (1%)

Results

24.0ms

256×

256

valid

Compiler

Compiled 10 to 5 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

composed: 10.0ms (53.3% of total)

ival-mult: 4.0ms (21.3% of total)

ival-add: 3.0ms (16% of total)

ival-sqrt: 2.0ms (10.7% of total)

const: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

prune2.0ms (0.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	2	2
Done	0	0
Total	2	2

Accuracy

100.0%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y z)
✓	98.8%	z

Compiler

Compiled 29 to 17 computations (41.4% saved)

regimes14.0ms (0.5%)

Counts

3 → 1

Calls

Call 1

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

Outputs
(hypot.f64 y z)

Calls

9 calls:

2.0ms	(+.f64 (.f64 x x) (.f64 y y))
2.0ms	y
2.0ms	z
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z 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 69 to 44 computations (36.2% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
z

Outputs
z

Calls

3 calls:

0.0ms	z
0.0ms	x
0.0ms	y

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`y`
98.8%	1	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17

Stop Event

1×

saturated

Calls

Call 1

Inputs
(hypot.f64 y z)
z

Outputs
(hypot.f64 y z)
z

soundness201.0ms (6.7%)

Rules

616×	`times-frac`
396×	`associate-+r+`
349×	`associate-+l+`
260×	`distribute-rgt-in`
259×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	485	12262
1	1300	10858
2	4180	10630

Stop Event

1×	done
1×	node limit

Compiler

Compiled 37 to 22 computations (40.5% saved)

preprocess77.0ms (2.6%)

Compiler: Compiled 192 to 122 computations (36.5% saved)

FRP.Yampa.Vector3:vector3Rho from Yampa-0.10.2

analyze2.0ms (0.1%)

sample1.5s (50.8%)

preprocess63.0ms (2.1%)

explain101.0ms (3.3%)

eval0.0ms (0%)

prune1.0ms (0%)

localize46.0ms (1.5%)

series13.0ms (0.4%)

rewrite444.0ms (14.7%)

simplify120.0ms (4%)

eval323.0ms (10.7%)

prune40.0ms (1.3%)

localize31.0ms (1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes14.0ms (0.5%)

regimes1.0ms (0%)

simplify2.0ms (0.1%)

soundness201.0ms (6.7%)

preprocess77.0ms (2.6%)

end0.0ms (0%)

Profiling