Metrics for sqrt A (should all be same)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 10 to 4 computations (60% saved)

sample844.0ms (31.2%)

Memory

-11.6MiB live, 774.2MiB allocated

Samples

425.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 219.0ms

ival-hypot: 209.0ms (95.5% of total)

ival-true: 6.0ms (2.7% of total)

ival-assert: 3.0ms (1.4% of total)

Bogosity

explain100.0ms (3.7%)

Memory

-1.9MiB live, 85.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
125	-	4	(-2.388101599777149e-157)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 x x))`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	oflow-rescue	70	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	overflow	70
↳	`(*.f64 x x)`	overflow	140
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	uflow-rescue	51	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	underflow	51
↳	`(*.f64 x x)`	underflow	102

Confusion

	Predicted +	Predicted -
+	121	4
-	0	131

Precision

1.0

Recall

0.968

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	121	0	4
-	0	0	131

Precision?

1.0

Recall?

0.968

Freqs

test

number	freq
0	135
1	121

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

64.0ms

512×

valid

Compiler

Compiled 51 to 16 computations (68.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-mult: 32.0ms (59.8% of total)

ival-hypot: 19.0ms (35.5% of total)

ival-add: 2.0ms (3.7% of total)

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

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

preprocess19.0ms (0.7%)

Memory

-1.7MiB live, 36.1MiB allocated

Algorithm

1×	egg-herbie

Rules

42×	`associate-r`
32×	`distribute-lft-neg-in`
32×	`sub-neg`
24×	`neg-sub0`
22×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	21	13
2	66	13
3	166	13
4	247	13
5	256	13
6	258	13
0	4	8
0	7	6
1	11	6
2	14	6
3	17	6
0	17	3

Stop Event

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

Calls

Call 1

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

Outputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(sqrt.f64 (*.f64 x (+.f64 x x)))

Symmetry

(abs x)

Compiler

Compiled 9 to 4 computations (55.6% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.1%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 9 to 4 computations (55.6% saved)

simplify4.0ms (0.1%)

Memory

5.6MiB live, 5.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
cost-diff	320	(+.f64 (.f64 x x) (.f64 x x))

Rules

14×	`lower-*.f32`
12×	`lower-*.f64`
4×	`*-commutative`
4×	`count-2`
4×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	19
0	7	15
1	11	15
2	14	15
3	17	15
0	17	12

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 x x)
x

localize18.0ms (0.7%)

Memory

23.3MiB live, 23.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.01171875	(+.f64 (.f64 x x) (.f64 x x))
accuracy	28.720279509494567	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Samples

12.0ms

256×

valid

Compiler

Compiled 21 to 6 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-hypot: 4.0ms (53.9% of total)

ival-mult: 2.0ms (26.9% of total)

ival-add: 1.0ms (13.5% of total)

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

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

series17.0ms (0.6%)

Memory

-33.3MiB live, 4.9MiB allocated

Counts

3 → 36

Calls

Call 1

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

Inputs

#s(alt (+.f64 (*.f64 x x) (*.f64 x x)) (patch (+.f64 (*.f64 x x) (*.f64 x x)) #<representation binary64>) () ())

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

#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())

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

Calls

9 calls:

Time	Variable		Point	Expression
14.0ms	x	@	inf	(+ (* x x) (* x x))
1.0ms	x	@	0	(sqrt (+ (* x x) (* x x)))
1.0ms	x	@	inf	(sqrt (+ (* x x) (* x x)))
1.0ms	x	@	0	(+ (* x x) (* x x))
0.0ms	x	@	-inf	(+ (* x x) (* x x))

simplify6.0ms (0.2%)

Memory

7.0MiB live, 7.0MiB allocated

Algorithm

1×	egg-herbie

Rules

38×	`lower-*.f64`
38×	`lower-fma.f64`
38×	`lower-fma.f32`
38×	`lower-*.f32`
36×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

Inputs
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite39.0ms (1.4%)

Memory

-4.0MiB live, 35.0MiB allocated

Rules

66×	`lower-*.f32`
64×	`lower-*.f64`
42×	`lower-fma.f64`
42×	`lower-fma.f32`
34×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	18
0	7	14
1	23	10
0	160	9

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

3 → 33

Calls

Call 1

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

Outputs
(+.f64 (.f64 x x) (.f64 x x))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 0 binary64)) (/.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 0 binary64)))
(fma.f64 x x (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (neg.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))))
(*.f64 x (+.f64 x x))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(*.f64 (+.f64 x x) x)
(exp.f64 (.f64 (log.f64 (.f64 x (+.f64 x x))) #s(literal 1/2 binary64)))
(hypot.f64 x x)
(hypot.f64 x (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) x)
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(pow.f64 (*.f64 x (+.f64 x x)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 x x)))
(.f64 (pow.f64 (.f64 x (+.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x (+.f64 x x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))

eval8.0ms (0.3%)

Memory: 11.9MiB live, 11.9MiB allocated
Compiler: Compiled 750 to 94 computations (87.5% saved)

prune11.0ms (0.4%)

Memory

-13.9MiB live, 23.8MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	80	5	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	5	86

Accuracy

100.0%

Counts

86 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	15.9%	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
▶	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	55.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 102 to 50 computations (51% saved)

simplify16.0ms (0.6%)

Memory

27.4MiB live, 27.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
cost-diff	64	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
cost-diff	1280	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
cost-diff	0	(+.f64 x x)
cost-diff	0	(sqrt.f64 (+.f64 x x))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
cost-diff	0	(+.f64 x x)
cost-diff	0	(*.f64 (+.f64 x x) x)
cost-diff	0	(sqrt.f64 (*.f64 (+.f64 x x) x))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
cost-diff	5312	(hypot.f64 x x)

Rules

352×	`lower-*.f32`
340×	`lower-*.f64`
308×	`lower-fma.f32`
306×	`lower-fma.f64`
294×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	136
0	40	122
1	55	110
2	102	95
3	188	89
4	253	89
5	522	89
6	557	89
7	558	89
0	558	89

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(hypot.f64 x x)
x
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 (+.f64 x x) x))
(*.f64 (+.f64 x x) x)
(+.f64 x x)
x
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 x)
x
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(*.f64 x x)
x
#s(literal 0 binary64)
(*.f64 x (+.f64 x x))
(+.f64 x x)
(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))

Outputs
(hypot.f64 x x)
(sqrt.f64 (*.f64 x (+.f64 x x)))
x
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 (+.f64 x x) x))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(*.f64 (+.f64 x x) x)
(*.f64 x (+.f64 x x))
(+.f64 x x)
x
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 x)
x
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
(/.f64 (sqrt.f64 (.f64 (.f64 x x) (.f64 (+.f64 x x) (.f64 x (.f64 x x))))) (.f64 x x))
(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
(sqrt.f64 (.f64 (.f64 x x) (.f64 (+.f64 x x) (.f64 x (*.f64 x x)))))
(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
(.f64 (.f64 x x) (.f64 (+.f64 x x) (.f64 x (*.f64 x x))))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(.f64 x (.f64 x (*.f64 x x)))
(*.f64 x x)
x
#s(literal 0 binary64)
(*.f64 x (+.f64 x x))
(+.f64 x x)
(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
(*.f64 x x)

localize73.0ms (2.7%)

Memory

-23.7MiB live, 137.1MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.14681625976844204	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	10.201376984594058	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
accuracy	15.682878782327645	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
accuracy	41.106233173137	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
accuracy	0	(+.f64 x x)
accuracy	0	(sqrt.f64 (+.f64 x x))
accuracy	0	(sqrt.f64 x)
accuracy	0.328125	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
accuracy	0	(+.f64 x x)
accuracy	0	(*.f64 (+.f64 x x) x)
accuracy	28.720279509494567	(sqrt.f64 (*.f64 (+.f64 x x) x))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.42578125	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.0234375	(hypot.f64 x x)

Samples

43.0ms

256×

valid

Compiler

Compiled 149 to 22 computations (85.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-sqrt: 13.0ms (41.1% of total)

ival-mult: 10.0ms (31.6% of total)

ival-hypot: 5.0ms (15.8% of total)

ival-div: 2.0ms (6.3% of total)

ival-add: 2.0ms (6.3% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.3%)

Memory

22.1MiB live, 22.1MiB allocated

Counts

14 → 156

Calls

Call 1

Inputs
#s(alt (hypot.f64 x x) (patch (hypot.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ ( x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (+.f64 x x) x)) (patch (sqrt.f64 (.f64 (+.f64 x x) x)) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 x x) x) (patch (.f64 (+.f64 x x) x) #<representation binary64>) () ())
#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) #<representation binary64>) () ())

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

Calls

39 calls:

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

simplify246.0ms (9.1%)

Memory

-7.9MiB live, 114.8MiB allocated

Algorithm

1×	egg-herbie

Rules

1 808×	`lower-*.f64`
1 808×	`lower-fma.f64`
1 808×	`lower-fma.f32`
1 808×	`lower-*.f32`
1 768×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	664
1	63	664
2	168	664
3	337	664
4	579	664
5	920	664
6	1535	664
7	1673	664
8	1758	664
9	1845	664
10	1911	664
11	1956	664
12	1972	664
13	1976	664
14	1976	664
15	2080	664
16	2339	664
17	2781	664
18	3397	664
19	3463	664
20	3577	664
21	3635	664
22	3695	664
23	4027	664
24	4163	664
25	4163	664
26	4163	664
27	4163	664
28	4639	664
29	4811	664
30	4847	664
31	4861	664
32	4863	664
33	4863	664
34	5067	664
0	5067	664

Stop Event

1×	iter limit
1×	saturated

Counts

156 → 156

Calls

Call 1

Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))

Outputs
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))

rewrite46.0ms (1.7%)

Memory

1.8MiB live, 78.4MiB allocated

Rules

168×	`lower-*.f32`
164×	`lower-*.f64`
134×	`lower-fma.f32`
132×	`lower-fma.f64`
112×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	101
0	40	51
1	109	29
0	828	29

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

14 → 60

Calls

Call 1

Inputs
(hypot.f64 x x)
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(*.f64 (+.f64 x x) x)
(+.f64 x x)
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 x)
(sqrt.f64 (+.f64 x x))
(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))

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

eval31.0ms (1.1%)

Memory: -0.9MiB live, 75.0MiB allocated
Compiler: Compiled 4 677 to 286 computations (93.9% saved)

prune17.0ms (0.6%)

Memory

11.7MiB live, 50.8MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	278	3	281
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	279	7	286

Accuracy

100.0%

Counts

286 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	17.1%	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	55.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	99.1%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
▶	3.7%	#s(literal 0 binary64)

Compiler

Compiled 57 to 33 computations (42.1% saved)

simplify42.0ms (1.6%)

Memory

-12.4MiB live, 27.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
cost-diff	0	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
cost-diff	64	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
cost-diff	0	(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
cost-diff	0	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
cost-diff	12480	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Rules

352×	`lower-*.f32`
342×	`lower-*.f64`
308×	`lower-fma.f32`
306×	`lower-fma.f64`
304×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	130
0	35	121
1	53	98
2	109	81
3	203	75
4	264	75
5	532	75
6	567	75
7	568	75
0	568	72

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
x
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/2 binary64)
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(*.f64 x x)
x
#s(literal 0 binary64)
(*.f64 x (+.f64 x x))
(+.f64 x x)
#s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x))

Outputs
#s(literal 0 binary64)
#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/2 binary64)
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
(/.f64 (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x (+.f64 x x))))))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
(sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x (+.f64 x x)))))))
(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
(.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x (+.f64 x x))))))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(.f64 x (.f64 x (*.f64 x x)))
(*.f64 x x)
x
#s(literal 0 binary64)
(*.f64 x (+.f64 x x))
(+.f64 x x)
#s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x))

localize68.0ms (2.5%)

Memory

-8.6MiB live, 114.1MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.046875	(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
accuracy	0.14681625976844204	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	10.201376984594058	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
accuracy	41.106233173137	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
accuracy	0	(log.f64 #s(literal 2 binary64))
accuracy	0	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
accuracy	0.42578125	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
accuracy	1.0	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Samples

46.0ms

256×

valid

Compiler

Compiled 122 to 20 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-mult: 8.0ms (29.9% of total)

ival-hypot: 5.0ms (18.7% of total)

ival-sqrt: 4.0ms (15% of total)

ival-exp: 3.0ms (11.2% of total)

ival-log: 3.0ms (11.2% of total)

ival-add: 2.0ms (7.5% of total)

ival-div: 1.0ms (3.7% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

6.0MiB live, 6.0MiB allocated

Counts

9 → 72

Calls

Call 1

Inputs
#s(alt (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (patch (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (patch (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))) (patch (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))) #<representation binary64>) () ())
#s(alt (log.f64 #s(literal 2 binary64)) (patch (log.f64 #s(literal 2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
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Calls

18 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))
0.0ms	x	@	inf	(* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))
0.0ms	x	@	0	(* x (exp (* (log 2) 1/2)))
0.0ms	x	@	-inf	(* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))
0.0ms	x	@	inf	(sqrt (+ (* x x) (* x x)))

simplify11.0ms (0.4%)

Memory

21.0MiB live, 21.0MiB allocated

Algorithm

1×	egg-herbie

Rules

122×	`lower-*.f64`
122×	`lower-*.f32`
118×	`lower-fma.f64`
118×	`lower-fma.f32`
56×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	324
1	29	324
2	60	324
3	107	324
4	126	324
5	167	324
6	201	324
7	230	324
8	260	324
9	262	324
0	262	324

Stop Event

1×	iter limit
1×	saturated

Counts

72 → 72

Calls

Call 1

Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))

Outputs
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x))))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))

rewrite117.0ms (4.3%)

Memory

-21.3MiB live, 135.4MiB allocated

Rules

2 658×	`lower-fma.f32`
2 656×	`lower-fma.f64`
2 078×	`lower-*.f32`
2 074×	`lower-*.f64`
1 004×	`lower-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	100
0	35	50
1	98	21
2	755	18
3	4627	18
0	8580	18

Stop Event

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

Counts

9 → 174

Calls

Call 1

Inputs
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
(log.f64 #s(literal 2 binary64))

Outputs
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal 2 binary64))
(pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))))
#s(approx (sqrt (+ (* x x) (* x x))) #s(literal 0 binary64))
#s(literal 0 binary64)
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
(+.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))
(+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 8 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -4 binary64) (log.f64 x)) #s(literal -1 binary64)))
(fabs.f64 (.f64 x (.f64 x (*.f64 x x))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))
(-.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(sqrt.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))
(fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x x)) x #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x x)) (neg.f64 x) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) (.f64 x (.f64 x (*.f64 x (sqrt.f64 x)))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) (sqrt.f64 (neg.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal 0 binary64))
(fma.f64 (.f64 x (sqrt.f64 x)) (.f64 x (*.f64 x (sqrt.f64 x))) #s(literal 0 binary64))
(fma.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 (neg.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x)))))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x))))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (sqrt.f64 x))) (*.f64 x (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 0 binary64))
(fma.f64 (neg.f64 x) (.f64 x (.f64 x x)) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (.f64 x (.f64 x (sqrt.f64 x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (.f64 x (sqrt.f64 x))) (sqrt.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (*.f64 x (sqrt.f64 x)))) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal 0 binary64))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))) #s(literal 0 binary64))
(fma.f64 (/.f64 x (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))) (/.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal 0 binary64))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 x)))) (sqrt.f64 x) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 x)))) (sqrt.f64 (neg.f64 x)) #s(literal 0 binary64))
(fma.f64 (.f64 (neg.f64 x) (.f64 x (sqrt.f64 x))) (*.f64 x (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (sqrt.f64 x)))))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (sqrt.f64 (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))))) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (sqrt.f64 (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 x (.f64 x (.f64 x (sqrt.f64 x))))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (neg.f64 x)) (.f64 x (.f64 x (*.f64 x (sqrt.f64 x)))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (neg.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (sqrt.f64 x) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (neg.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (*.f64 x (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 x (sqrt.f64 x)))) (sqrt.f64 (*.f64 x (sqrt.f64 x))) #s(literal 0 binary64))
(neg.f64 (.f64 x (.f64 x (*.f64 x x))))
(/.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1 binary64)))
(/.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x))))
(/.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) x)
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (.f64 x (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x x)))))
(/.f64 (pow.f64 x #s(literal 36 binary64)) (pow.f64 (*.f64 x x) #s(literal 16 binary64)))
(/.f64 (pow.f64 x #s(literal 24 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))
(/.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))))
(/.f64 (.f64 x (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))))
(/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))
(/.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 x x)))
(/.f64 (pow.f64 (*.f64 x x) #s(literal 14 binary64)) (pow.f64 x #s(literal 24 binary64)))
(/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(/.f64 (.f64 (.f64 x (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal 1 binary64)) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))
(/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))
(pow.f64 x #s(literal 4 binary64))
(pow.f64 (*.f64 x x) #s(literal 2 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1 binary64))
(pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))
(pow.f64 (.f64 x (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))) #s(literal 1/4 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (exp.f64 #s(literal 4 binary64)) (log.f64 x))
(.f64 x (.f64 x (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 x x))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))
(.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))
(.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))))
(.f64 (.f64 x (*.f64 x x)) x)
(.f64 (.f64 x (*.f64 x x)) (neg.f64 x))
(.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))
(.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x))
(.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))
(.f64 (sqrt.f64 x) (.f64 x (.f64 x (.f64 x (sqrt.f64 x)))))
(.f64 (sqrt.f64 x) (sqrt.f64 (neg.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (.f64 x (sqrt.f64 x)) (.f64 x (.f64 x (sqrt.f64 x))))
(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 (neg.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))))))
(.f64 (.f64 x (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (.f64 x (.f64 x (sqrt.f64 x))) (.f64 x (sqrt.f64 x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))
(.f64 (neg.f64 x) (.f64 x (*.f64 x x)))
(.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))
(.f64 (.f64 x (.f64 x (.f64 x (*.f64 x (sqrt.f64 x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 x))) (sqrt.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 x (sqrt.f64 x)))))
(.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))))
(.f64 (/.f64 x (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))) (/.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (.f64 x (.f64 x (.f64 x (sqrt.f64 x)))) (sqrt.f64 x))
(.f64 (.f64 x (.f64 x (.f64 x (sqrt.f64 x)))) (sqrt.f64 (neg.f64 x)))
(.f64 (.f64 (neg.f64 x) (.f64 x (sqrt.f64 x))) (.f64 x (sqrt.f64 x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))
(.f64 (sqrt.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(.f64 (sqrt.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (*.f64 x (sqrt.f64 x)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (sqrt.f64 (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))))) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (sqrt.f64 (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 x (.f64 x (*.f64 x (sqrt.f64 x))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (sqrt.f64 (neg.f64 x)) (.f64 x (.f64 x (.f64 x (sqrt.f64 x)))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (.f64 x x))))
(.f64 (sqrt.f64 (neg.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))) (sqrt.f64 x))
(.f64 (sqrt.f64 (neg.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (sqrt.f64 x)))
(.f64 (sqrt.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 x (sqrt.f64 x)))) (sqrt.f64 (.f64 x (sqrt.f64 x))))
#s(literal 0 binary64)
#s(literal 0 binary64)
#s(literal 0 binary64)
(log.f64 #s(literal 2 binary64))

eval26.0ms (0.9%)

Memory: 9.8MiB live, 46.8MiB allocated
Compiler: Compiled 6 339 to 765 computations (87.9% saved)

prune26.0ms (0.9%)

Memory

14.8MiB live, 53.3MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	244	2	246
Fresh	0	0	0
Picked	2	1	3
Done	0	4	4
Total	246	7	253

Accuracy

100.0%

Counts

253 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	17.1%	(/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
▶	33.4%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	55.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	3.7%	#s(literal 0 binary64)

Compiler

Compiled 70 to 34 computations (51.4% saved)

simplify148.0ms (5.5%)

Memory

-20.6MiB live, 157.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x)))
cost-diff	0	(sqrt.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x))))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
cost-diff	1664	(/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
cost-diff	0	#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
cost-diff	0	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))

Rules

4 964×	`lower-*.f32`
4 952×	`lower-*.f64`
4 102×	`lower-fma.f64`
4 102×	`lower-fma.f32`
2 654×	`lower-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	236
0	37	182
1	70	142
2	223	112
3	837	110
4	1706	110
5	4861	110
6	6477	110
0	8113	110

Stop Event

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

Calls

Call 1

Inputs
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 x (.f64 x x))
x
(*.f64 x x)
#s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x))
(/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
(sqrt.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x))))
(.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x)))
(/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x))
(.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))
(.f64 x (.f64 x x))
x
(*.f64 x x)
(*.f64 x (+.f64 x x))
(+.f64 x x)
#s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x))

Outputs
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 x (.f64 x x))
x
(*.f64 x x)
#s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x))
(/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
(/.f64 (sqrt.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
(sqrt.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x))))
(sqrt.f64 (.f64 x (.f64 (.f64 x (.f64 x (*.f64 x x))) (+.f64 x x))))
(.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x)))
(.f64 x (.f64 (.f64 x (.f64 x (*.f64 x x))) (+.f64 x x)))
(/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x))
(.f64 x (.f64 x (*.f64 x x)))
(.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))
(.f64 x (.f64 x x))
x
(*.f64 x x)
(*.f64 x (+.f64 x x))
(+.f64 x x)
#s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x))

localize148.0ms (5.5%)

Memory

8.1MiB live, 89.9MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.1015625	(.f64 x (.f64 x x))
accuracy	10.201376984594058	(sqrt.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x))))
accuracy	32.06820670683461	(/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x))
accuracy	41.106233173137	(/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
accuracy	0	#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
accuracy	0.1015625	(.f64 x (.f64 x x))
accuracy	0.18035126953688402	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
accuracy	41.106233173137	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))

Samples

36.0ms

256×

valid

Compiler

Compiled 204 to 22 computations (89.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-mult: 12.0ms (46.3% of total)

ival-sqrt: 6.0ms (23.2% of total)

ival-div: 4.0ms (15.4% of total)

ival-add: 2.0ms (7.7% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.3%)

Memory

-27.2MiB live, 10.8MiB allocated

Counts

9 → 96

Calls

Call 1

Inputs
#s(alt (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) (patch #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (patch (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x)))) (patch (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x)))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x))) (patch (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x))) #<representation binary64>) () ())
#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())

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

Calls

24 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	inf	(* x (* x x))
0.0ms	x	@	-inf	(* (sqrt 2) (* x (* x x)))
0.0ms	x	@	0	(* (sqrt 2) (* x (* x x)))
0.0ms	x	@	inf	(* (sqrt 2) (* x (* x x)))

simplify12.0ms (0.5%)

Memory

19.8MiB live, 19.8MiB allocated

Algorithm

1×	egg-herbie

Rules

122×	`lower-*.f64`
122×	`lower-*.f32`
118×	`lower-fma.f64`
118×	`lower-fma.f32`
56×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	460
1	29	460
2	60	460
3	107	460
4	125	460
5	166	460
6	200	460
7	229	460
8	259	460
9	261	460
0	261	460

Stop Event

1×	iter limit
1×	saturated

Counts

96 → 96

Calls

Call 1

Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)

Outputs
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))

rewrite148.0ms (5.5%)

Memory

-7.9MiB live, 146.2MiB allocated

Rules

3 278×	`lower-fma.f64`
3 278×	`lower-fma.f32`
2 640×	`lower-*.f32`
2 632×	`lower-*.f64`
1 420×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	175
0	37	105
1	122	46
2	893	41
3	6079	41
0	8435	41

Stop Event

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

Counts

9 → 419

Calls

Call 1

Inputs
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(sqrt.f64 #s(literal 2 binary64))
(/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x))
(/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
(sqrt.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x))))
(.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x)))
(.f64 x (.f64 x x))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (.f64 x x)) #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))))
(neg.f64 (neg.f64 (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))))
(neg.f64 (.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x)) #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))))))
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
(/.f64 (neg.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x))))) (neg.f64 #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x)) #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))))
(/.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x))) (/.f64 #s(literal 1 binary64) #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x)) #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))))) (neg.f64 #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))))
(/.f64 (.f64 (neg.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (neg.f64 #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))))
(/.f64 (/.f64 (neg.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x))))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
(pow.f64 (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x)) #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))))
(.f64 (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #s(literal 1 binary64))
(.f64 (neg.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x))))) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))))
(.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (.f64 x x))) #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (.f64 x x))) (pow.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))))
(.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (.f64 x x))) (neg.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))))
(.f64 (pow.f64 (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (.f64 x x))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))))) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))))
(neg.f64 (neg.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))))
#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
(.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))))
(.f64 #s(literal -1 binary64) (neg.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)) (*.f64 #s(literal 3 binary64) (log.f64 x))))
(exp.f64 (fma.f64 #s(literal 3 binary64) (log.f64 x) (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))))
(pow.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 x (sqrt.f64 x))) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 x (sqrt.f64 x)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) #s(literal 2 binary64))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 x (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 x (.f64 x x))))
(.f64 (.f64 x (sqrt.f64 x)) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 #s(literal 2 binary64))))
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(/.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))
(/.f64 (.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))
(/.f64 (.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 x (.f64 x (*.f64 x x)))))
(/.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (.f64 x x))
(/.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))))
(/.f64 (.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 3/4 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(pow.f64 (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x))))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 3/8 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -3/4 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -3/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -3 binary64))
(pow.f64 (*.f64 x (sqrt.f64 x)) #s(literal 2 binary64))
(pow.f64 (/.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (*.f64 x x))))) #s(literal -1 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(.f64 (.f64 x x) x)
(.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64))
(.f64 (.f64 x (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) x) x))
(.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))) x))
(.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x))))))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x (.f64 x x)))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))
(.f64 (sqrt.f64 x) (.f64 x (*.f64 x (sqrt.f64 x))))
(.f64 (.f64 x (*.f64 x (sqrt.f64 x))) (sqrt.f64 x))
(.f64 (.f64 x (sqrt.f64 x)) (*.f64 x (sqrt.f64 x)))
(.f64 (.f64 x (sqrt.f64 x)) (neg.f64 (*.f64 x (sqrt.f64 x))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (*.f64 x x)))
(.f64 (neg.f64 (.f64 x (sqrt.f64 x))) (*.f64 x (sqrt.f64 x)))

eval122.0ms (4.5%)

Memory: 26.7MiB live, 137.1MiB allocated
Compiler: Compiled 22 161 to 2 534 computations (88.6% saved)

prune92.0ms (3.4%)

Memory

-5.5MiB live, 197.4MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	699	2	701
Fresh	0	0	0
Picked	1	1	2
Done	0	5	5
Total	700	8	708

Accuracy

100.0%

Counts

708 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
	33.4%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x)) x)) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
	33.4%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (/.f64 #s(literal 1 binary64) (.f64 x x))))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
✓	33.4%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	55.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	3.7%	#s(literal 0 binary64)

Compiler

Compiled 229 to 83 computations (63.8% saved)

regimes21.0ms (0.8%)

Memory

4.5MiB live, 40.4MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x)) x)) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (/.f64 #s(literal 1 binary64) (.f64 x x))))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
(/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
(hypot.f64 x x)
#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))

Outputs
(hypot.f64 x x)

Calls

4 calls:

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

Results

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

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes21.0ms (0.8%)

Memory

-5.7MiB live, 34.4MiB allocated

Counts

11 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x)) x)) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (/.f64 #s(literal 1 binary64) (.f64 x x))))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
(/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))

Outputs
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))

Calls

4 calls:

9.0ms	(+.f64 (.f64 x x) (.f64 x x))
4.0ms	x
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
4.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.5%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.5%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes9.0ms (0.4%)

Memory

-18.5MiB live, 18.8MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Outputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Calls

4 calls:

3.0ms	x
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	(+.f64 (.f64 x x) (.f64 x x))
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.3%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.3%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes5.0ms (0.2%)

Memory

14.5MiB live, 14.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

4 calls:

1.0ms	x
1.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
1.0ms	(+.f64 (.f64 x x) (.f64 x x))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
3.7%	1	`x`
3.7%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
3.7%	1	`(+.f64 (.f64 x x) (.f64 x x))`
3.7%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify5.0ms (0.2%)

Memory

12.3MiB live, 12.3MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	16	24

Stop Event

1×

saturated

Calls

Call 1

Inputs
(hypot.f64 x x)
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
#s(literal 0 binary64)

Outputs
(hypot.f64 x x)
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
#s(literal 0 binary64)

soundness110.0ms (4%)

Memory

-4.1MiB live, 111.2MiB allocated

Rules

168×	`lower-*.f32`
164×	`lower-*.f64`
134×	`lower-fma.f32`
132×	`lower-fma.f64`
112×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	101
0	40	51
1	109	29
0	828	29
0	4	18
0	7	14
1	23	10
0	160	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

Stop Event

1×	fuel
1×	iter limit
1×	saturated
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Compiler

Compiled 67 to 35 computations (47.8% saved)

preprocess59.0ms (2.2%)

Memory: -2.6MiB live, 72.1MiB allocated
Remove: (abs x)
Compiler: Compiled 60 to 32 computations (46.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	6	13
1	21	13
2	66	13
3	166	13
4	247	13
5	256	13
6	258	13
0	4	8
0	7	6
1	11	6
2	14	6
3	17	6
0	17	3

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

Iter	Nodes	Cost
0	23	136
0	40	122
1	55	110
2	102	95
3	188	89
4	253	89
5	522	89
6	557	89
7	558	89
0	558	89

Iter	Nodes	Cost
0	15	324
1	29	324
2	60	324
3	107	324
4	126	324
5	167	324
6	201	324
7	230	324
8	260	324
9	262	324
0	262	324

Iter	Nodes	Cost
0	15	460
1	29	460
2	60	460
3	107	460
4	125	460
5	166	460
6	200	460
7	229	460
8	259	460
9	261	460
0	261	460

Iter	Nodes	Cost
0	23	101
0	40	51
1	109	29
0	828	29
0	4	18
0	7	14
1	23	10
0	160	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

Iter	Nodes	Cost
0	6	13
1	21	13
2	66	13
3	166	13
4	247	13
5	256	13
6	258	13
0	4	8
0	7	6
1	11	6
2	14	6
3	17	6
0	17	3

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

Iter	Nodes	Cost
0	23	136
0	40	122
1	55	110
2	102	95
3	188	89
4	253	89
5	522	89
6	557	89
7	558	89
0	558	89

Iter	Nodes	Cost
0	15	324
1	29	324
2	60	324
3	107	324
4	126	324
5	167	324
6	201	324
7	230	324
8	260	324
9	262	324
0	262	324

Iter	Nodes	Cost
0	15	460
1	29	460
2	60	460
3	107	460
4	125	460
5	166	460
6	200	460
7	229	460
8	259	460
9	261	460
0	261	460

Iter	Nodes	Cost
0	23	101
0	40	51
1	109	29
0	828	29
0	4	18
0	7	14
1	23	10
0	160	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

start0.0ms (0%)

analyze0.0ms (0%)

sample844.0ms (31.2%)

explain100.0ms (3.7%)

preprocess19.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize18.0ms (0.7%)

series17.0ms (0.6%)

simplify6.0ms (0.2%)

rewrite39.0ms (1.4%)

eval8.0ms (0.3%)

prune11.0ms (0.4%)

simplify16.0ms (0.6%)

localize73.0ms (2.7%)

series9.0ms (0.3%)

simplify246.0ms (9.1%)

rewrite46.0ms (1.7%)

eval31.0ms (1.1%)

prune17.0ms (0.6%)

simplify42.0ms (1.6%)

localize68.0ms (2.5%)

series3.0ms (0.1%)

simplify11.0ms (0.4%)

rewrite117.0ms (4.3%)

eval26.0ms (0.9%)

prune26.0ms (0.9%)

simplify148.0ms (5.5%)

localize148.0ms (5.5%)

series8.0ms (0.3%)

simplify12.0ms (0.5%)

rewrite148.0ms (5.5%)

eval122.0ms (4.5%)

prune92.0ms (3.4%)

regimes21.0ms (0.8%)

regimes21.0ms (0.8%)

regimes9.0ms (0.4%)

regimes5.0ms (0.2%)

simplify5.0ms (0.2%)

soundness110.0ms (4%)

preprocess59.0ms (2.2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	13
1	21	13
2	66	13
3	166	13
4	247	13
5	256	13
6	258	13
0	4	8
0	7	6
1	11	6
2	14	6
3	17	6
0	17	3

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

Iter	Nodes	Cost
0	23	136
0	40	122
1	55	110
2	102	95
3	188	89
4	253	89
5	522	89
6	557	89
7	558	89
0	558	89

Iter	Nodes	Cost
0	15	324
1	29	324
2	60	324
3	107	324
4	126	324
5	167	324
6	201	324
7	230	324
8	260	324
9	262	324
0	262	324

Iter	Nodes	Cost
0	15	460
1	29	460
2	60	460
3	107	460
4	125	460
5	166	460
6	200	460
7	229	460
8	259	460
9	261	460
0	261	460

Iter	Nodes	Cost
0	23	101
0	40	51
1	109	29
0	828	29
0	4	18
0	7	14
1	23	10
0	160	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148