Metrics for Data.Octree.Internal:octantDistance from Octree-0.5.4.2

analyze1.0ms (0%)

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
100%	99.9%	0%	0.1%	0%	0%	0%	3

Compiler

Compiled 11 to 7 computations (36.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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)

backward-pass: 0.0ms (0% of total)

sample1.3s (64.1%)

Results

1.0s

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 799.0ms

ival-mult: 474.0ms (59.3% of total)

ival-sqrt: 271.0ms (33.9% of total)

ival-add: 44.0ms (5.5% of total)

const: 7.0ms (0.9% of total)

backward-pass: 3.0ms (0.4% of total)

Bogosity

preprocess50.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

52×	`fma-neg`
45×	`fma-define`
15×	`distribute-lft-neg-in`
15×	`neg-sub0`
14×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	99
1	51	99
2	98	99
3	185	99
4	282	99
5	321	99
6	331	99

Stop Event

1×

saturated

Calls

Call 1

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

Outputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
(hypot.f64 x y)
(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
(hypot.f64 x y)
(sqrt.f64 (+.f64 (.f64 (neg.f64 x) (neg.f64 x)) (.f64 y y)))
(hypot.f64 x y)
(sqrt.f64 (+.f64 (.f64 x x) (.f64 (neg.f64 y) (neg.f64 y))))
(hypot.f64 x y)
(neg.f64 (sqrt.f64 (+.f64 (.f64 (neg.f64 x) (neg.f64 x)) (.f64 y y))))
(neg.f64 (hypot.f64 x y))
(neg.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 (neg.f64 y) (neg.f64 y)))))
(neg.f64 (hypot.f64 x y))
(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))
(hypot.f64 x y)

Symmetry

(abs x)

(abs y)

(sort x y)

explain63.0ms (3.1%)

FPErrors

Click to see full error table

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

Results

38.0ms

512×

valid

Compiler

Compiled 62 to 20 computations (67.7% saved)

Precisions

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

ival-mult: 12.0ms (62.4% of total)

ival-sqrt: 4.0ms (20.8% of total)

ival-add: 3.0ms (15.6% of total)

const: 1.0ms (5.2% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 5 to 3 computations (40% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 5 to 3 computations (40% saved)

localize24.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(hypot.f64 x y)
✓	accuracy	100.0%	(hypot.f64 x y)

Rules

2×	`fma-define`
1×	`hypot-define`
1×	`hypot-undefine`
1×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	13	21
2	16	21
3	18	21

Stop Event

1×

saturated

Calls

Call 1

Inputs
(hypot.f64 x y)
x
y

Outputs
(hypot.f64 x y)
x
y

Results

13.0ms

256×

valid

Compiler

Compiled 8 to 4 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-hypot: 5.0ms (99.8% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series5.0ms (0.2%)

Counts

1 → 24

Calls

Call 1

Inputs
#<alt (hypot.f64 x y)>

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(sqrt (+ (* x x) (* y y)))
1.0ms	x	@	0	(sqrt (+ (* x x) (* y y)))
1.0ms	y	@	inf	(sqrt (+ (* x x) (* y y)))
1.0ms	y	@	0	(sqrt (+ (* x x) (* y y)))
0.0ms	y	@	-inf	(sqrt (+ (* x x) (* y y)))

rewrite294.0ms (14.6%)

Algorithm

1×	batch-egg-rewrite

Rules

425×	`log1p-expm1-u`
294×	`associate-r`
244×	`expm1-log1p-u`
242×	`associate-l`
232×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	66	13
2	696	13
3	7648	13

Stop Event

1×	node limit

Counts

1 → 58

Calls

Call 1

Inputs
(hypot.f64 x y)

Outputs
(+.f64 (+.f64 (hypot.f64 x y) #s(literal 1 binary64)) #s(literal -1 binary64))
(+.f64 #s(literal 0 binary64) (hypot.f64 x y))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x y))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x y)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x y)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x y)))))
(-.f64 (+.f64 (hypot.f64 x y) #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 (hypot.f64 x y) #s(literal 1 binary64))
(*.f64 (hypot.f64 x y) (log.f64 (E.f64)))
(*.f64 #s(literal 1 binary64) (hypot.f64 x y))
(*.f64 (cbrt.f64 (hypot.f64 x y)) (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 2 binary64)))
(*.f64 (cbrt.f64 (hypot.f64 x y)) (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 2 binary64)) (cbrt.f64 (hypot.f64 x y)))
(*.f64 (sqrt.f64 (hypot.f64 x y)) (sqrt.f64 (hypot.f64 x y)))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x y))) #s(literal 2 binary64)) (.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x y))) (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 2 binary64))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 4 binary64))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x y))) #s(literal 2 binary64)) (cbrt.f64 (hypot.f64 x y))))
(.f64 (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64)) (.f64 (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64)) (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (hypot.f64 x y) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (hypot.f64 x y) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (hypot.f64 x y) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (hypot.f64 x y) #s(literal 3/2 binary64))))
(.f64 (pow.f64 (hypot.f64 x y) #s(literal 1/4 binary64)) (.f64 (pow.f64 (hypot.f64 x y) #s(literal 1/4 binary64)) (sqrt.f64 (hypot.f64 x y))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (hypot.f64 x y))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 4 binary64)) #s(literal 1/2 binary64)) (cbrt.f64 (hypot.f64 x y)))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x y) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (hypot.f64 x y) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 5 binary64)) #s(literal 1/2 binary64)) (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (hypot.f64 x y))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (hypot.f64 x y))))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x y) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64)))
(.f64 (.f64 (sqrt.f64 (hypot.f64 x y)) (cbrt.f64 (hypot.f64 x y))) (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 4 binary64)) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (hypot.f64 x y))))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x y) #s(literal 5/2 binary64))) (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64)))
(.f64 (.f64 (sqrt.f64 (hypot.f64 x y)) (pow.f64 (hypot.f64 x y) #s(literal 1/4 binary64))) (pow.f64 (hypot.f64 x y) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (hypot.f64 x y) #s(literal 3/2 binary64))) (pow.f64 (hypot.f64 x y) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 5 binary64))) (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64)))
(.f64 (.f64 (cbrt.f64 (hypot.f64 x y)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 4 binary64)))) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x y))) #s(literal 2 binary64)))
(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x y))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (hypot.f64 x y))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 2 binary64)) (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64))) (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (sqrt.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (+.f64 (hypot.f64 x y) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (*.f64 (+.f64 (hypot.f64 x y) #s(literal 1 binary64)) (+.f64 (hypot.f64 x y) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (hypot.f64 x y) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (+.f64 (hypot.f64 x y) #s(literal 1 binary64)) (+.f64 (hypot.f64 x y) #s(literal 1 binary64))) #s(literal 1 binary64)) (+.f64 (+.f64 (hypot.f64 x y) #s(literal 1 binary64)) #s(literal 1 binary64)))
(pow.f64 (hypot.f64 x y) #s(literal 1 binary64))
(pow.f64 (pow.f64 (hypot.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (hypot.f64 x y) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (hypot.f64 x y)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (hypot.f64 x y)))
(pow.f64 (pow.f64 (hypot.f64 x y) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (hypot.f64 x y)) #s(literal 2 binary64)))) (cbrt.f64 (log.f64 (hypot.f64 x y))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 x y)))) (sqrt.f64 (log.f64 (hypot.f64 x y))))
(sqrt.f64 (pow.f64 (hypot.f64 x y) #s(literal 2 binary64)))
(fabs.f64 (hypot.f64 x y))
(log.f64 (exp.f64 (hypot.f64 x y)))
(cbrt.f64 (pow.f64 (hypot.f64 x y) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (hypot.f64 x y)))
(log1p.f64 (expm1.f64 (hypot.f64 x y)))
(exp.f64 (log.f64 (hypot.f64 x y)))
(exp.f64 (.f64 (.f64 (log.f64 (hypot.f64 x y)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x y))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 (hypot.f64 x y))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x y))) #s(literal 2 binary64)))

simplify92.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

724×	`fma-define`
466×	`distribute-lft-in`
435×	`distribute-rgt-in`
255×	`fma-neg`
245×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	251	3078
1	560	3018
2	1710	2984
3	5781	2898

Stop Event

1×	node limit

Counts

82 → 164

Calls

Call 1

Inputs
y
(+.f64 y (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) y)))
(+.f64 y (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) y)))))
(+.f64 y (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 (.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) y)))))
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 y #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 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 y #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 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 y #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 (pow.f64 y #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 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 y #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 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))))))))
x
(+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) x)))
(+.f64 x (.f64 (pow.f64 y #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)))))
(+.f64 x (.f64 (pow.f64 y #s(literal 2 binary64)) (+.f64 (.f64 (pow.f64 y #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)))))
y
(.f64 y (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #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 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #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 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (+.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #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 (pow.f64 x #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 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #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 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (+.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64)))))))))
(+.f64 (+.f64 (hypot.f64 x y) #s(literal 1 binary64)) #s(literal -1 binary64))
(+.f64 #s(literal 0 binary64) (hypot.f64 x y))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x y))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x y)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x y)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x y)))))
(-.f64 (+.f64 (hypot.f64 x y) #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 (hypot.f64 x y) #s(literal 1 binary64))
(*.f64 (hypot.f64 x y) (log.f64 (E.f64)))
(*.f64 #s(literal 1 binary64) (hypot.f64 x y))
(*.f64 (cbrt.f64 (hypot.f64 x y)) (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 2 binary64)))
(*.f64 (cbrt.f64 (hypot.f64 x y)) (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 2 binary64)) (cbrt.f64 (hypot.f64 x y)))
(*.f64 (sqrt.f64 (hypot.f64 x y)) (sqrt.f64 (hypot.f64 x y)))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x y))) #s(literal 2 binary64)) (.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x y))) (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 2 binary64))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 4 binary64))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x y))) #s(literal 2 binary64)) (cbrt.f64 (hypot.f64 x y))))
(.f64 (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64)) (.f64 (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64)) (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (hypot.f64 x y) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (hypot.f64 x y) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (hypot.f64 x y) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (hypot.f64 x y) #s(literal 3/2 binary64))))
(.f64 (pow.f64 (hypot.f64 x y) #s(literal 1/4 binary64)) (.f64 (pow.f64 (hypot.f64 x y) #s(literal 1/4 binary64)) (sqrt.f64 (hypot.f64 x y))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (hypot.f64 x y))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 4 binary64)) #s(literal 1/2 binary64)) (cbrt.f64 (hypot.f64 x y)))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x y) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (hypot.f64 x y) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 5 binary64)) #s(literal 1/2 binary64)) (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (hypot.f64 x y))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (hypot.f64 x y))))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x y) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64)))
(.f64 (.f64 (sqrt.f64 (hypot.f64 x y)) (cbrt.f64 (hypot.f64 x y))) (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 4 binary64)) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (hypot.f64 x y))))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x y) #s(literal 5/2 binary64))) (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64)))
(.f64 (.f64 (sqrt.f64 (hypot.f64 x y)) (pow.f64 (hypot.f64 x y) #s(literal 1/4 binary64))) (pow.f64 (hypot.f64 x y) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (hypot.f64 x y) #s(literal 3/2 binary64))) (pow.f64 (hypot.f64 x y) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 5 binary64))) (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64)))
(.f64 (.f64 (cbrt.f64 (hypot.f64 x y)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 4 binary64)))) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x y))) #s(literal 2 binary64)))
(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x y))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (hypot.f64 x y))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 2 binary64)) (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64))) (pow.f64 (hypot.f64 x y) #s(literal 1/6 binary64)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (sqrt.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (+.f64 (hypot.f64 x y) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (*.f64 (+.f64 (hypot.f64 x y) #s(literal 1 binary64)) (+.f64 (hypot.f64 x y) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (hypot.f64 x y) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (+.f64 (hypot.f64 x y) #s(literal 1 binary64)) (+.f64 (hypot.f64 x y) #s(literal 1 binary64))) #s(literal 1 binary64)) (+.f64 (+.f64 (hypot.f64 x y) #s(literal 1 binary64)) #s(literal 1 binary64)))
(pow.f64 (hypot.f64 x y) #s(literal 1 binary64))
(pow.f64 (pow.f64 (hypot.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (cbrt.f64 (hypot.f64 x y)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (hypot.f64 x y) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (hypot.f64 x y)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (hypot.f64 x y)))
(pow.f64 (pow.f64 (hypot.f64 x y) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (hypot.f64 x y)) #s(literal 2 binary64)))) (cbrt.f64 (log.f64 (hypot.f64 x y))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 x y)))) (sqrt.f64 (log.f64 (hypot.f64 x y))))
(sqrt.f64 (pow.f64 (hypot.f64 x y) #s(literal 2 binary64)))
(fabs.f64 (hypot.f64 x y))
(log.f64 (exp.f64 (hypot.f64 x y)))
(cbrt.f64 (pow.f64 (hypot.f64 x y) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (hypot.f64 x y)))
(log1p.f64 (expm1.f64 (hypot.f64 x y)))
(exp.f64 (log.f64 (hypot.f64 x y)))
(exp.f64 (.f64 (.f64 (log.f64 (hypot.f64 x y)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x y))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 (hypot.f64 x y))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x y))) #s(literal 2 binary64)))

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

eval21.0ms (1%)

Compiler: Compiled 2682 to 462 computations (82.8% saved)

prune22.0ms (1.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	163	2	165

Accuracy

100.0%

Counts

165 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x y)
▶	99.6%	y

Compiler

Compiled 8 to 5 computations (37.5% saved)

localize12.0ms (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4

Stop Event

1×

saturated

Calls

Call 1

Inputs
y

Outputs
y

Results

5.0ms

256×

valid

Compiler

Compiled 4 to 3 computations (25% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune7.0ms (0.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	1	1
Total	2	2

Accuracy

100.0%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x y)
✓	99.6%	y

Compiler

Compiled 22 to 12 computations (45.5% saved)

regimes20.0ms (1%)

Counts

3 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x y)

Calls

6 calls:

2.0ms	x
2.0ms	y
2.0ms	(*.f64 y y)
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

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

Compiler

Compiled 35 to 21 computations (40% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
y

Outputs
y

Calls

2 calls:

1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify3.0ms (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 x y)
y

Outputs
(hypot.f64 x y)
y

soundness23.0ms (1.1%)

Rules

52×	`fma-neg`
45×	`fma-define`
15×	`distribute-lft-neg-in`
15×	`neg-sub0`
14×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	99
1	51	99
2	98	99
3	185	99
4	282	99
5	321	99
6	331	99

Stop Event

1×	done
1×	saturated

Compiler

Compiled 19 to 10 computations (47.4% saved)

preprocess83.0ms (4.1%)

Remove

(sort x y)

(abs y)

(abs x)

Compiler

Compiled 164 to 98 computations (40.2% saved)

Data.Octree.Internal:octantDistance from Octree-0.5.4.2

analyze1.0ms (0%)

sample1.3s (64.1%)

preprocess50.0ms (2.5%)

explain63.0ms (3.1%)

eval0.0ms (0%)

prune1.0ms (0%)

localize24.0ms (1.2%)

series5.0ms (0.2%)

rewrite294.0ms (14.6%)

simplify92.0ms (4.6%)

eval21.0ms (1%)

prune22.0ms (1.1%)

localize12.0ms (0.6%)

eval0.0ms (0%)

prune7.0ms (0.4%)

regimes20.0ms (1%)

regimes3.0ms (0.1%)

simplify3.0ms (0.1%)

soundness23.0ms (1.1%)

preprocess83.0ms (4.1%)

end0.0ms (0%)

Profiling