Metrics for sqrt A (should all be same)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB 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)

sample2.0s (54.2%)

Memory

13.1MiB live, 521.9MiB allocated

Samples

1.8s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 191.0ms

ival-hypot: 183.0ms (95.8% of total)

ival-true: 5.0ms (2.6% of total)

ival-assert: 3.0ms (1.6% of total)

Bogosity

explain71.0ms (1.9%)

Memory

4.9MiB live, 154.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
127	-	3	(-7.189682313890562e-158)	`(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	69	0
↳	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	overflow	1
↳	`(+.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	55	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	underflow	55
↳	`(*.f64 x x)`	underflow	110

Confusion

	Predicted +	Predicted -
+	124	4
-	0	128

Precision

1.0

Recall

0.96875

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	124	0	4
-	0	0	128

Precision?

1.0

Recall?

0.96875

Freqs

test

number	freq
0	132
1	124

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

25.0ms

512×

valid

Compiler

Compiled 50 to 16 computations (68% saved)

Precisions

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

ival-hypot: 8.0ms (54.4% of total)

ival-mult: 4.0ms (27.2% of total)

ival-add: 2.0ms (13.6% of total)

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

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

preprocess19.0ms (0.5%)

Memory

5.5MiB live, 43.7MiB 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	4

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 (hypot.f64 x x))

Symmetry

(abs x)

Compiler

Compiled 8 to 4 computations (50% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.4%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 8 to 4 computations (50% saved)

simplify3.0ms (0.1%)

Memory

7.5MiB live, 7.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	-5632	(+.f64 (.f64 x x) (.f64 x x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(sqrt.f64 (+.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	11

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 (hypot.f64 x x))
(+.f64 (.f64 x x) (.f64 x x))
(hypot.f64 x x)
(*.f64 x x)
x

localize19.0ms (0.5%)

Memory

4.7MiB live, 42.9MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(+.f64 (.f64 x x) (.f64 x x))
accuracy	29.167785908597242	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Samples

14.0ms

256×

valid

Compiler

Compiled 21 to 6 computations (71.4% saved)

Precisions

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

ival-mult: 4.0ms (41.6% of total)

ival-hypot: 4.0ms (41.6% of total)

ival-add: 1.0ms (10.4% of total)

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

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

series4.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Counts

3 → 36

Calls

Call 1

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

Inputs

#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>) () ())

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

Outputs
#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 (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 (* 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 (* 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 (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 (* 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 (* -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 -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 (* 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>) () ())) ())

Calls

3 calls:

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

simplify6.0ms (0.2%)

Memory

10.1MiB live, 10.1MiB 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	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

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

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

rewrite42.0ms (1.1%)

Memory

-35.2MiB live, 52.7MiB allocated

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

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

Counts

3 → 33

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 x x)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) x) x)
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 x (.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 x x (*.f64 x x))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) x)
(hypot.f64 x (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 x x)
(+.f64 (.f64 x x) (.f64 x x))

eval8.0ms (0.2%)

Memory: 17.0MiB live, 17.0MiB allocated
Compiler: Compiled 673 to 111 computations (83.5% saved)

prune3.0ms (0.1%)

Memory

9.8MiB live, 9.8MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	3	86

Accuracy

99.9%

Counts

86 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
▶	54.4%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
▶	99.4%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 18 to 16 computations (11.1% saved)

simplify7.0ms (0.2%)

Memory

-30.3MiB live, 8.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal 2 binary64) x)
cost-diff	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
cost-diff	-5824	(.f64 (.f64 x x) #s(literal 2 binary64))
cost-diff	0	(*.f64 x x)
cost-diff	0	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Rules

22×	`lower-*.f32`
12×	`lower-*.f64`
10×	`lift-*.f64`
8×	`lift-sqrt.f64`
8×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	55
0	24	53
1	32	53
2	33	53
0	33	47

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize38.0ms (1%)

Memory

33.0MiB live, 71.3MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 2 binary64) x)
accuracy	0	(sqrt.f64 x)
accuracy	0.23827791536057094	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
accuracy	0.33041000976844204	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(.f64 (.f64 x x) #s(literal 2 binary64))
accuracy	29.167785908597242	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
accuracy	0.39453125	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Samples

28.0ms

256×

valid

Compiler

Compiled 52 to 14 computations (73.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 7.0ms (41.3% of total)

ival-sqrt: 6.0ms (35.4% of total)

ival-hypot: 4.0ms (23.6% of total)

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

exact: 0.0ms (0% of total)

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

series15.0ms (0.4%)

Memory

-26.1MiB live, 16.1MiB allocated

Counts

10 → 108

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

7.0ms

((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* (* x x) 2)) (* x x) (* (* x x) 2) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x))

3.0ms

-inf

((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* (* x x) 2)) (* x x) (* (* x x) 2) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x))

2.0ms

inf

((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* (* x x) 2)) (* x x) (* (* x x) 2) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x))

simplify138.0ms (3.8%)

Memory

22.6MiB live, 57.9MiB allocated

Algorithm

1×	egg-herbie

Rules

1 460×	`associate-r`
1 232×	`lower-*.f64`
1 232×	`lower-fma.f64`
1 232×	`lower-fma.f32`
1 232×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	448
1	50	448
2	136	448
3	263	448
4	491	448
5	809	448
6	1420	448
7	1546	448
8	1601	448
9	1639	448
10	1822	448
11	2036	448
12	2080	448
13	2108	448
14	2112	448
15	2112	448
16	2253	448
17	2437	448
18	3518	448
19	3636	448
20	3660	448
21	3668	448
22	3672	448
23	3676	448
24	3788	448
25	3836	448
26	3836	448
27	4001	448
0	4001	448

Stop Event

1×	iter limit
1×	saturated

Counts

108 → 108

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

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

rewrite34.0ms (0.9%)

Memory

4.1MiB live, 41.0MiB allocated

Rules

90×	`lower-*.f32`
80×	`lower-*.f64`
42×	`lower-fma.f64`
42×	`lower-fma.f32`
38×	`lower-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	49
0	24	46
1	52	38
0	202	38

Stop Event

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

Counts

10 → 65

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #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)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (.f64 #s(literal 2 binary64) x) x)
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 x (.f64 #s(literal 2 binary64) x))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 x x))
(fma.f64 x x (*.f64 x x))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)))
(hypot.f64 (fabs.f64 x) (fabs.f64 x))
(hypot.f64 (fabs.f64 x) x)
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x x)
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) (-.f64 x x))
(+.f64 x x)

eval20.0ms (0.6%)

Memory: 8.7MiB live, 46.5MiB allocated
Compiler: Compiled 1 258 to 173 computations (86.2% saved)

prune28.0ms (0.8%)

Memory

-25.5MiB live, 32.8MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	171	5	176

Accuracy

100.0%

Counts

176 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
▶	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	54.4%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	99.4%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	99.1%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))

Compiler

Compiled 38 to 31 computations (18.4% saved)

simplify5.0ms (0.1%)

Memory

6.4MiB live, 6.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
cost-diff	0	(pow.f64 x #s(literal 1/4 binary64))
cost-diff	0	(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
cost-diff	12608	(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
cost-diff	-128	(+.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 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
cost-diff	12480	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Rules

36×	`lower-*.f32`
26×	`lower-*.f64`
14×	`*-commutative`
12×	`lift-*.f64`
8×	`lower-sqrt.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	86
0	34	68
1	51	65
2	60	65
0	60	63

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
(.f64 (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)
x
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 x)
x
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 x #s(literal 1/4 binary64))
x
#s(literal 1/4 binary64)
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)

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

localize61.0ms (1.7%)

Memory

5.2MiB live, 81.3MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(pow.f64 x #s(literal 1/4 binary64))
accuracy	0.23827791536057094	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
accuracy	0.33041000976844204	(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
accuracy	0.49447250976844204	(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
accuracy	0	(+.f64 x x)
accuracy	0	(sqrt.f64 x)
accuracy	0.23827791536057094	(sqrt.f64 (+.f64 x x))
accuracy	0.33041000976844204	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
accuracy	0	(log.f64 #s(literal 2 binary64))
accuracy	0	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
accuracy	0.39453125	(.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
accuracy	1.0	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Samples

45.0ms

256×

valid

Compiler

Compiled 80 to 20 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-mult: 12.0ms (35.6% of total)

ival-sqrt: 5.0ms (14.9% of total)

ival-pow: 5.0ms (14.9% of total)

ival-hypot: 4.0ms (11.9% of total)

ival-exp: 3.0ms (8.9% of total)

ival-log: 3.0ms (8.9% of total)

ival-add: 1.0ms (3% of total)

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

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

exact: 0.0ms (0% of total)

series69.0ms (1.9%)

Memory

-25.7MiB live, 92.2MiB allocated

Counts

13 → 120

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

Calls

3 calls:

Time

Variable

Point

Expression

31.0ms

((exp (* (log 2) 1/2)) (sqrt (+ (* x x) (* x x))) (* (exp (* (log 2) 1/2)) x) (* (log 2) 1/2) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (+ x x) (* (pow x 1/4) (pow x 1/4)) (* (* (pow x 1/4) (pow x 1/4)) (sqrt (* 2 x))) (pow x 1/4) (sqrt (* 2 x)) (log 2))

23.0ms

-inf

((exp (* (log 2) 1/2)) (sqrt (+ (* x x) (* x x))) (* (exp (* (log 2) 1/2)) x) (* (log 2) 1/2) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (+ x x) (* (pow x 1/4) (pow x 1/4)) (* (* (pow x 1/4) (pow x 1/4)) (sqrt (* 2 x))) (pow x 1/4) (sqrt (* 2 x)) (log 2))

7.0ms

inf

((exp (* (log 2) 1/2)) (sqrt (+ (* x x) (* x x))) (* (exp (* (log 2) 1/2)) x) (* (log 2) 1/2) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (+ x x) (* (pow x 1/4) (pow x 1/4)) (* (* (pow x 1/4) (pow x 1/4)) (sqrt (* 2 x))) (pow x 1/4) (sqrt (* 2 x)) (log 2))

simplify302.0ms (8.3%)

Memory

11.0MiB live, 86.5MiB allocated

Algorithm

1×	egg-herbie

Rules

1 408×	`lower-fma.f64`
1 408×	`lower-fma.f32`
1 244×	`lower-*.f64`
1 244×	`lower-*.f32`
1 082×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	500
1	73	500
2	203	500
3	403	500
4	650	500
5	1012	500
6	1746	500
7	2166	500
8	2989	500
9	3160	500
10	3262	500
11	3295	500
12	3304	500
13	3304	500
14	3434	500
15	3731	500
16	3887	500
17	4728	500
18	5283	500
19	5663	500
20	5843	500
21	5908	500
22	6111	500
23	6832	500
24	7163	500
25	7311	500
26	7457	500
27	7603	500
28	7749	500
29	7904	500
30	7904	500
31	7928	500
32	7928	500
33	7928	500
0	7928	500

Stop Event

1×	iter limit
1×	saturated

Counts

120 → 120

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))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt 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))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt 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))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -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)))
(* -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))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 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)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(* -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))))

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

rewrite46.0ms (1.3%)

Memory

9.2MiB live, 54.1MiB allocated

Rules

152×	`lower-*.f32`
142×	`lower-*.f64`
72×	`lower-fma.f64`
72×	`lower-fma.f32`
56×	`lower-pow.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	76
0	34	60
1	83	47
0	327	47

Stop Event

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

Counts

13 → 143

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 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
(.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 x)
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(pow.f64 x #s(literal 1/4 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(log.f64 #s(literal 2 binary64))

Outputs
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 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)
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 x #s(literal 2 binary64)))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 x #s(literal 2 binary64))))))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x #s(literal 2 binary64))))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 x #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 x x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64))))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1/4 binary64) (*.f64 (log.f64 x) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 x #s(literal 2 binary64)))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 x #s(literal 2 binary64))))))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x #s(literal 2 binary64))))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 x #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 x x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64))))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64))))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(.f64 (.f64 x #s(literal 2 binary64)) x)
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 x (.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 x x))
(*.f64 #s(literal 2 binary64) x)
(/.f64 (.f64 x (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64)))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 x x (*.f64 x x))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)))
(-.f64 (/.f64 (.f64 x x) #s(literal 0 binary64)) (/.f64 (.f64 x x) #s(literal 0 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) x)
(hypot.f64 x (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 x x)
(+.f64 (.f64 x x) (.f64 x x))
(+.f64 x x)
(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1/4 binary64) (*.f64 (log.f64 x) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 x #s(literal 2 binary64)))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 x #s(literal 2 binary64))))))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x #s(literal 2 binary64))))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 x #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 x x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64))))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 1/8 binary64)))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/8 binary64))
(pow.f64 x #s(literal 1/4 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/4 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 x #s(literal 2 binary64)))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 x #s(literal 2 binary64))))))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x #s(literal 2 binary64))))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 x #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 x x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64))))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(log.f64 #s(literal 2 binary64))

eval27.0ms (0.8%)

Memory: 6.7MiB live, 45.1MiB allocated
Compiler: Compiled 2 891 to 319 computations (89% saved)

prune13.0ms (0.3%)

Memory

-12.8MiB live, 25.2MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	278	3	281
Fresh	0	0	0
Picked	1	2	3
Done	0	2	2
Total	279	7	286

Accuracy

100.0%

Counts

286 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x)))
▶	99.0%	(.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	99.0%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
✓	54.4%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	99.4%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	99.1%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))

Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify39.0ms (1.1%)

Memory

-10.0MiB live, 28.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (+.f64 x x))
cost-diff	0	(pow.f64 x #s(literal 1/4 binary64))
cost-diff	0	(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x)))
cost-diff	12288	(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
cost-diff	0	(pow.f64 x #s(literal 1/8 binary64))
cost-diff	0	(.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
cost-diff	6464	(pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64))
cost-diff	12608	(*.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
cost-diff	1600	(*.f64 (sqrt.f64 x) (sqrt.f64 x))

Rules

1 200×	`lower-*.f32`
1 190×	`lower-*.f64`
1 088×	`associate-r`
630×	`associate-l`
344×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	92
0	34	82
1	50	64
2	75	62
3	102	62
4	198	62
5	556	62
6	1234	62
7	1318	62
8	1331	62
9	1331	62
10	1331	62
11	1452	62
12	1453	62
13	1454	62
0	1454	62

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(sqrt.f64 x)
x
(.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal 1/8 binary64))
x
#s(literal 1/8 binary64)
#s(literal 2 binary64)
(pow.f64 x #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x)))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal 1/4 binary64))
x
#s(literal 1/4 binary64)
#s(literal 2 binary64)
(sqrt.f64 (+.f64 x x))
(+.f64 x x)

Outputs
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
x
(sqrt.f64 x)
x
(.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(sqrt.f64 x)
(pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal 1/4 binary64))
(pow.f64 x #s(literal 1/8 binary64))
x
#s(literal 1/8 binary64)
#s(literal 2 binary64)
(pow.f64 x #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x)))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 x)
(pow.f64 x #s(literal 1/4 binary64))
x
#s(literal 1/4 binary64)
#s(literal 2 binary64)
(sqrt.f64 (+.f64 x x))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(+.f64 x x)
(*.f64 x #s(literal 2 binary64))

localize61.0ms (1.7%)

Memory

26.3MiB live, 66.9MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(pow.f64 x #s(literal 1/4 binary64))
accuracy	0.23827791536057094	(sqrt.f64 (+.f64 x x))
accuracy	0.33041000976844204	(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x)))
accuracy	0.49447250976844204	(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
accuracy	0.23827791536057094	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
accuracy	0.33041000976844204	(.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
accuracy	0.48275375976844204	(pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64))
accuracy	0.49447250976844204	(*.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
accuracy	0	(sqrt.f64 x)
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.39453125	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
accuracy	0.48046875	(*.f64 (sqrt.f64 x) (sqrt.f64 x))

Samples

47.0ms

256×

valid

Compiler

Compiled 94 to 21 computations (77.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-pow: 10.0ms (30% of total)

ival-mult: 8.0ms (24% of total)

ival-pow2: 7.0ms (21% of total)

ival-sqrt: 6.0ms (18% of total)

ival-add: 1.0ms (3% of total)

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

exact: 0.0ms (0% of total)

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

series78.0ms (2.2%)

Memory

-34.7MiB live, 42.4MiB allocated

Counts

13 → 144

Calls

Call 1

Inputs
#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 x) (sqrt.f64 x)) #<representation:binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) #<representation:binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation:binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation:binary64>) () ())
#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) #<representation:binary64>) () ())
#s(alt (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())
#s(alt (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) (patch (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) #<representation:binary64>) () ())
#s(alt (pow.f64 x #s(literal 1/8 binary64)) (patch (pow.f64 x #s(literal 1/8 binary64)) #<representation:binary64>) () ())
#s(alt (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())
#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) #<representation:binary64>) () ())
#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation:binary64>) () ())
#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation:binary64>) () ())
#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())

Outputs
#s(alt x (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 x) (sqrt.f64 x)) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 x) (sqrt.f64 x)) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 x) (sqrt.f64 x)) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 x) (sqrt.f64 x)) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/4) (taylor 0 x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/4) (taylor 0 x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/4) (taylor 0 x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/4) (taylor 0 x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) (patch (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) (patch (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) (patch (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) (patch (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/8) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 1/8 binary64)) (patch (pow.f64 x #s(literal 1/8 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/8) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 1/8 binary64)) (patch (pow.f64 x #s(literal 1/8 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/8) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 1/8 binary64)) (patch (pow.f64 x #s(literal 1/8 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/8) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 1/8 binary64)) (patch (pow.f64 x #s(literal 1/8 binary64)) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/4) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/4) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/4) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/4) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 x) (sqrt.f64 x)) #<representation:binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 x) (sqrt.f64 x)) #<representation:binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 x) (sqrt.f64 x)) #<representation:binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 x) (sqrt.f64 x)) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/4) (taylor inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/4) (taylor inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/4) (taylor inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/4) (taylor inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) (patch (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) (patch (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) (patch (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) (patch (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/8) (taylor inf x) (#s(alt (pow.f64 x #s(literal 1/8 binary64)) (patch (pow.f64 x #s(literal 1/8 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/8) (taylor inf x) (#s(alt (pow.f64 x #s(literal 1/8 binary64)) (patch (pow.f64 x #s(literal 1/8 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/8) (taylor inf x) (#s(alt (pow.f64 x #s(literal 1/8 binary64)) (patch (pow.f64 x #s(literal 1/8 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/8) (taylor inf x) (#s(alt (pow.f64 x #s(literal 1/8 binary64)) (patch (pow.f64 x #s(literal 1/8 binary64)) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/4) (taylor inf x) (#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/4) (taylor inf x) (#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/4) (taylor inf x) (#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/4) (taylor inf x) (#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 x) (sqrt.f64 x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 x) (sqrt.f64 x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 x) (sqrt.f64 x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 x) (sqrt.f64 x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) #<representation:binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) (patch (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) (patch (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) (patch (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) (patch (.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) #<representation:binary64>) () ())) ())
#s(alt (exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 1/8 binary64)) (patch (pow.f64 x #s(literal 1/8 binary64)) #<representation:binary64>) () ())) ())
#s(alt (exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 1/8 binary64)) (patch (pow.f64 x #s(literal 1/8 binary64)) #<representation:binary64>) () ())) ())
#s(alt (exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 1/8 binary64)) (patch (pow.f64 x #s(literal 1/8 binary64)) #<representation:binary64>) () ())) ())
#s(alt (exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 1/8 binary64)) (patch (pow.f64 x #s(literal 1/8 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) (patch (.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation:binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation:binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation:binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

56.0ms

((* (sqrt x) (sqrt x)) (* (sqrt 2) (* (sqrt x) (sqrt x))) (sqrt 2) (sqrt x) (* (pow (pow x 1/8) 2) (pow x 1/4)) (pow (pow x 1/8) 2) (* (* (pow (pow x 1/8) 2) (pow x 1/4)) (sqrt (* 2 x))) (pow x 1/8) (pow (pow x 1/4) 2) (* (pow (pow x 1/4) 2) (sqrt (+ x x))) (pow x 1/4) (sqrt (+ x x)) (sqrt (* 2 x)))

9.0ms

-inf

((* (sqrt x) (sqrt x)) (* (sqrt 2) (* (sqrt x) (sqrt x))) (sqrt 2) (sqrt x) (* (pow (pow x 1/8) 2) (pow x 1/4)) (pow (pow x 1/8) 2) (* (* (pow (pow x 1/8) 2) (pow x 1/4)) (sqrt (* 2 x))) (pow x 1/8) (pow (pow x 1/4) 2) (* (pow (pow x 1/4) 2) (sqrt (+ x x))) (pow x 1/4) (sqrt (+ x x)) (sqrt (* 2 x)))

7.0ms

inf

((* (sqrt x) (sqrt x)) (* (sqrt 2) (* (sqrt x) (sqrt x))) (sqrt 2) (sqrt x) (* (pow (pow x 1/8) 2) (pow x 1/4)) (pow (pow x 1/8) 2) (* (* (pow (pow x 1/8) 2) (pow x 1/4)) (sqrt (* 2 x))) (pow x 1/8) (pow (pow x 1/4) 2) (* (pow (pow x 1/4) 2) (sqrt (+ x x))) (pow x 1/4) (sqrt (+ x x)) (sqrt (* 2 x)))

simplify225.0ms (6.2%)

Memory

10.9MiB live, 92.6MiB allocated

Algorithm

1×	egg-herbie

Rules

1 504×	`lower-fma.f64`
1 504×	`lower-fma.f32`
1 240×	`lower-*.f64`
1 240×	`lower-*.f32`
828×	`associate-*r/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	520
1	96	520
2	287	520
3	649	520
4	1006	520
5	1576	520
6	2244	520
7	2786	520
8	3343	520
9	3524	520
10	3640	520
11	3824	520
12	3900	520
13	4440	520
14	4540	520
15	4613	520
16	4669	520
17	4677	520
18	4677	520
19	4689	520
20	4689	520
21	4689	520
0	4689	520

Stop Event

1×	iter limit
1×	saturated

Counts

144 → 136

Calls

Call 1

Inputs
x
x
x
x
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(pow (* 1 x) 1/8)
(pow (* 1 x) 1/8)
(pow (* 1 x) 1/8)
(pow (* 1 x) 1/8)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(* (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))
x
x
x
x
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(pow (* 1 x) 1/8)
(pow (* 1 x) 1/8)
(pow (* 1 x) 1/8)
(pow (* 1 x) 1/8)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(* (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 (* x (pow (sqrt -1) 2)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(* -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)))
(* -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)))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 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)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(* -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))))
(* -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))))

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

rewrite35.0ms (1%)

Memory

24.6MiB live, 24.6MiB allocated

Rules

178×	`lower-*.f32`
168×	`lower-*.f64`
88×	`lower-pow.f32`
80×	`lower-pow.f64`
64×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	74
0	34	38
1	90	38
0	348	38

Stop Event

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

Counts

13 → 151

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64))
(.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(pow.f64 x #s(literal 1/8 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x)))
(pow.f64 x #s(literal 1/4 binary64))
(sqrt.f64 (+.f64 x x))
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))

Outputs
(.f64 (.f64 (sqrt.f64 x) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 1 binary64))
(sqrt.f64 (*.f64 x x))
(fabs.f64 x)
(exp.f64 (fma.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64) (.f64 (*.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
(exp.f64 (.f64 (.f64 (*.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 2 binary64)))
x
(.f64 (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 1/4 binary64))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 1/4 binary64)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) x) #s(literal 1/2 binary64))
(pow.f64 (.f64 x (.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
(sqrt.f64 (.f64 x (.f64 #s(literal 2 binary64) x)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(fabs.f64 (sqrt.f64 x))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1/4 binary64) (*.f64 (log.f64 x) #s(literal 1/4 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(fabs.f64 (sqrt.f64 x))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1/4 binary64) (*.f64 (log.f64 x) #s(literal 1/4 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 1/16 binary64))) (pow.f64 x #s(literal 1/16 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 x #s(literal 1/16 binary64)) (pow.f64 x #s(literal 1/8 binary64))))
(*.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 1/8 binary64)))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(pow.f64 x #s(literal 1/4 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/4 binary64)))
(.f64 (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 1/4 binary64))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 1/4 binary64)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) x) #s(literal 1/2 binary64))
(pow.f64 (.f64 x (.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
(sqrt.f64 (.f64 x (.f64 #s(literal 2 binary64) x)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/16 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/16 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1/16 binary64)) (pow.f64 x #s(literal 1/16 binary64)))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 x #s(literal 1/16 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/16 binary64))
(pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1/4 binary64))
(pow.f64 x #s(literal 1/8 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/8 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/8 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(fabs.f64 (sqrt.f64 x))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1/4 binary64) (*.f64 (log.f64 x) #s(literal 1/4 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(.f64 (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 1/4 binary64))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 1/4 binary64)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) x) #s(literal 1/2 binary64))
(pow.f64 (.f64 x (.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
(sqrt.f64 (.f64 x (.f64 #s(literal 2 binary64) x)))
(.f64 (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 1/16 binary64))) (pow.f64 x #s(literal 1/16 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 x #s(literal 1/16 binary64)) (pow.f64 x #s(literal 1/8 binary64))))
(*.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 1/8 binary64)))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(pow.f64 x #s(literal 1/4 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/4 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))

eval80.0ms (2.2%)

Memory: -11.7MiB live, 63.2MiB allocated
Compiler: Compiled 3 779 to 383 computations (89.9% saved)

prune16.0ms (0.4%)

Memory

-4.3MiB live, 33.8MiB allocated

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	334	3	337
Fresh	0	0	0
Picked	1	2	3
Done	0	4	4
Total	335	9	344

Accuracy

100.0%

Counts

344 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.6%	(*.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 4 binary64)) (sqrt.f64 (+.f64 x x)))
✓	99.0%	(.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
	99.0%	(.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (+.f64 x x)))
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	98.8%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 x)))
✓	99.0%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
✓	54.4%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	99.4%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	99.1%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))

Compiler

Compiled 203 to 107 computations (47.3% saved)

regimes16.0ms (0.4%)

Memory

25.1MiB live, 25.1MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (+.f64 x x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 x)))
#s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 4 binary64)) (sqrt.f64 (+.f64 x x)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (+.f64 x x)))
(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))

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

Calls

4 calls:

4.0ms	x
4.0ms	(+.f64 (.f64 x x) (.f64 x x))
4.0ms	(*.f64 x x)
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.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 19 to 10 computations (47.4% saved)

regimes9.0ms (0.3%)

Memory

-30.9MiB live, 12.1MiB allocated

Accuracy

Total -29.0b remaining (-7340.4%)

Threshold costs -29b (-7340.4%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

4 calls:

4.0ms	(*.f64 x x)
2.0ms	x
2.0ms	(+.f64 (.f64 x x) (.f64 x x))
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.4%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.4%	1	`(*.f64 x x)`

Compiler

Compiled 19 to 10 computations (47.4% saved)

simplify26.0ms (0.7%)

Memory

13.6MiB live, 52.5MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`-commutative-binary64-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	14	20

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness76.0ms (2.1%)

Memory

-4.5MiB live, 33.8MiB allocated

Rules

90×	`lower-*.f32`
80×	`lower-*.f64`
66×	`lower-*.f32`
64×	`lower-*.f64`
42×	`lower-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148
0	4	18
0	7	14
1	23	10
0	160	10
0	15	49
0	24	46
1	52	38
0	202	38

Stop Event

1×	fuel
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
1×	iter limit
1×	saturated

Compiler

Compiled 45 to 31 computations (31.1% saved)

preprocess26.0ms (0.7%)

Memory: 4.7MiB live, 43.0MiB allocated
Compiler: Compiled 68 to 46 computations (32.4% 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	4

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148
0	4	18
0	7	14
1	23	10
0	160	10
0	15	49
0	24	46
1	52	38
0	202	38

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	4

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148
0	4	18
0	7	14
1	23	10
0	160	10
0	15	49
0	24	46
1	52	38
0	202	38

start0.0ms (0%)

analyze0.0ms (0%)

sample2.0s (54.2%)

explain71.0ms (1.9%)

preprocess19.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize19.0ms (0.5%)

series4.0ms (0.1%)

simplify6.0ms (0.2%)

rewrite42.0ms (1.1%)

eval8.0ms (0.2%)

prune3.0ms (0.1%)

simplify7.0ms (0.2%)

localize38.0ms (1%)

series15.0ms (0.4%)

simplify138.0ms (3.8%)

rewrite34.0ms (0.9%)

eval20.0ms (0.6%)

prune28.0ms (0.8%)

simplify5.0ms (0.1%)

localize61.0ms (1.7%)

series69.0ms (1.9%)

simplify302.0ms (8.3%)

rewrite46.0ms (1.3%)

eval27.0ms (0.8%)

prune13.0ms (0.3%)

simplify39.0ms (1.1%)

localize61.0ms (1.7%)

series78.0ms (2.2%)

simplify225.0ms (6.2%)

rewrite35.0ms (1%)

eval80.0ms (2.2%)

prune16.0ms (0.4%)

regimes16.0ms (0.4%)

regimes9.0ms (0.3%)

simplify26.0ms (0.7%)

soundness76.0ms (2.1%)

preprocess26.0ms (0.7%)

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	4

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148
0	4	18
0	7	14
1	23	10
0	160	10
0	15	49
0	24	46
1	52	38
0	202	38