Metrics for sqrt A (should all be same)

analyze0.0ms (0%)

Memory

0.9MiB live, 0.9MiB 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)

sample503.0ms (17.8%)

Memory

23.1MiB live, 968.3MiB allocated

Samples

276.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 153.0ms

ival-hypot: 144.0ms (94.4% of total)

ival-true: 6.0ms (3.9% of total)

ival-assert: 3.0ms (2% of total)

Bogosity

preprocess18.0ms (0.6%)

Memory

7.0MiB live, 46.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

explain66.0ms (2.3%)

Memory

-14.9MiB live, 113.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
114	-	3	(7.11307426877938e-157)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 x x))`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	uflow-rescue	57	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	underflow	57
↳	`(*.f64 x x)`	underflow	114
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	oflow-rescue	54	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	overflow	54
↳	`(*.f64 x x)`	overflow	108

Confusion

	Predicted +	Predicted -
+	111	3
-	0	142

Precision

1.0

Recall

0.9736842105263158

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	111	0	3
-	0	0	142

Precision?

1.0

Recall?

0.9736842105263158

Freqs

test

number	freq
0	145
1	111

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

30.0ms

512×

valid

Compiler

Compiled 60 to 20 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-hypot: 13.0ms (65% of total)

ival-mult: 5.0ms (25% of total)

ival-add: 2.0ms (10% of total)

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

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

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.3%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 9 to 4 computations (55.6% saved)

simplify4.0ms (0.1%)

Memory

6.5MiB live, 6.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize19.0ms (0.7%)

Memory

-8.2MiB live, 30.8MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (.f64 x x) (.f64 x x))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	59.3%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Samples

13.0ms

256×

valid

Compiler

Compiled 21 to 6 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-hypot: 5.0ms (60.2% of total)

ival-add: 1.0ms (12% of total)

ival-mult: 1.0ms (12% of total)

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

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

series3.0ms (0.1%)

Memory

4.6MiB live, 4.6MiB allocated

Counts

3 → 36

Calls

Call 1

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

Outputs
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

9 calls:

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

simplify7.0ms (0.2%)

Memory

8.1MiB live, 8.1MiB 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	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

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

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

rewrite48.0ms (1.7%)

Memory

-8.6MiB live, 29.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

3 → 33

Calls

Call 1

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

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

eval8.0ms (0.3%)

Memory: 11.8MiB live, 11.8MiB allocated
Compiler: Compiled 702 to 94 computations (86.6% saved)

prune5.0ms (0.2%)

Memory

9.7MiB live, 9.7MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	4	86

Accuracy

100.0%

Counts

86 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	59.3%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 24 to 15 computations (37.5% saved)

simplify11.0ms (0.4%)

Memory

-31.4MiB live, 7.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	5312	(hypot.f64 x x)
✓	cost-diff	0	(+.f64 x x)
✓	cost-diff	0	(sqrt.f64 (+.f64 x x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	cost-diff	0	(+.f64 x x)
✓	cost-diff	0	(*.f64 (+.f64 x x) x)
✓	cost-diff	0	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	52
0	23	49
1	28	49
2	31	49
0	31	49

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize41.0ms (1.5%)

Memory

30.0MiB live, 69.8MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(hypot.f64 x x)
✓	accuracy	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	accuracy	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(*.f64 (+.f64 x x) x)
✓	accuracy	59.3%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))

Samples

27.0ms

256×

valid

Compiler

Compiled 59 to 13 computations (78% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-sqrt: 6.0ms (37.7% of total)

ival-mult: 4.0ms (25.1% of total)

ival-hypot: 4.0ms (25.1% of total)

ival-add: 1.0ms (6.3% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.2%)

Memory

-27.3MiB live, 10.9MiB allocated

Counts

10 → 108

Calls

Call 1

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

Outputs
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>

Calls

27 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(* (sqrt x) (sqrt (+ x x)))
0.0ms	x	@	-inf	(sqrt (+ x x))
0.0ms	x	@	inf	(* (+ x x) x)
0.0ms	x	@	-inf	(* x (sqrt 2))
0.0ms	x	@	inf	(+ x x)

simplify158.0ms (5.6%)

Memory

10.6MiB live, 129.7MiB allocated

Algorithm

1×	egg-herbie

Rules

1 478×	`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	464
1	50	464
2	136	464
3	265	464
4	490	464
5	809	464
6	1411	464
7	1537	464
8	1592	464
9	1630	464
10	1808	464
11	2022	464
12	2068	464
13	2096	464
14	2100	464
15	2100	464
16	2246	464
17	2430	464
18	3585	464
19	3703	464
20	3727	464
21	3735	464
22	3739	464
23	3743	464
24	3855	464
25	3903	464
26	3903	464
27	4085	464
0	4085	464

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

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

rewrite35.0ms (1.2%)

Memory

8.8MiB live, 46.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

98×	`lower-*.f32`
92×	`lower-*.f64`
68×	`lower-fma.f64`
68×	`lower-fma.f32`
58×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	44
0	23	38
1	51	34
0	255	34

Stop Event

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

Counts

10 → 127

Calls

Call 1

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

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

eval24.0ms (0.9%)

Memory: 19.6MiB live, 57.6MiB allocated
Compiler: Compiled 2 353 to 230 computations (90.2% saved)

prune17.0ms (0.6%)

Memory

-0.7MiB live, 36.7MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	270	3	273
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	270	7	277

Accuracy

100.0%

Counts

277 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	38.7%	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64)))))
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	7.2%	(sqrt.f64 (+.f64 x x))
✓	59.3%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	99.2%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify11.0ms (0.4%)

Memory

-33.4MiB live, 10.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64)))))
✓	cost-diff	64	(fma.f64 x x #s(literal 0 binary64))
✓	cost-diff	832	(sqrt.f64 (fma.f64 x x #s(literal 0 binary64)))
✓	cost-diff	0	(+.f64 x x)
✓	cost-diff	0	(sqrt.f64 (+.f64 x x))
✓	cost-diff	0	(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
✓	cost-diff	0	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
✓	cost-diff	12480	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Rules

50×	`lower-*.f32`
42×	`lower-*.f64`
32×	`lower-fma.f32`
30×	`lower-fma.f64`
22×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	111
0	34	95
1	53	78
2	93	78
3	112	78
4	113	78
0	113	75

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize96.0ms (3.4%)

Memory

27.8MiB live, 104.2MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.4%	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64)))))
✓	accuracy	73.8%	(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
✓	accuracy	67.7%	(sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)))
✓	accuracy	59.4%	(sqrt.f64 (fma.f64 x x #s(literal 0 binary64)))
✓	accuracy	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x x))
✓	accuracy	100.0%	(log.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
✓	accuracy	99.3%	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	98.4%	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Samples

51.0ms

256×

valid

Compiler

Compiled 113 to 21 computations (81.4% saved)

Precisions

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

ival-mult: 7.0ms (25.9% of total)

ival-sqrt: 6.0ms (22.2% of total)

ival-hypot: 4.0ms (14.8% of total)

ival-exp: 3.0ms (11.1% of total)

ival-log: 3.0ms (11.1% of total)

ival-div: 2.0ms (7.4% of total)

ival-add: 2.0ms (7.4% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

6.4MiB live, 6.4MiB allocated

Counts

13 → 120

Calls

Call 1

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

Outputs
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (pow x 3)) (sqrt 2))>
#<alt (* (sqrt (pow x 3)) (sqrt 2))>
#<alt (* (sqrt (pow x 3)) (sqrt 2))>
#<alt (* (sqrt (pow x 3)) (sqrt 2))>
#<alt (* (sqrt (pow x 3)) (sqrt 2))>
#<alt (* (sqrt (pow x 3)) (sqrt 2))>
#<alt (* (sqrt (pow x 3)) (sqrt 2))>
#<alt (* (sqrt (pow x 3)) (sqrt 2))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>

Calls

30 calls:

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

simplify197.0ms (6.9%)

Memory

-13.8MiB live, 142.2MiB allocated

Algorithm

1×	egg-herbie

Rules

1 488×	`lower-*.f64`
1 488×	`lower-fma.f64`
1 488×	`lower-fma.f32`
1 488×	`lower-*.f32`
1 348×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	524
1	61	524
2	152	524
3	280	524
4	526	524
5	854	524
6	1476	524
7	1669	524
8	1818	524
9	1904	524
10	1973	524
11	2028	524
12	2043	524
13	2045	524
14	2045	524
15	2185	524
16	2825	524
17	3099	524
18	3439	524
19	3481	524
20	3547	524
21	3581	524
22	3817	524
23	3897	524
24	3897	524
25	3897	524
26	4041	524
27	4351	524
28	4375	524
0	4375	524

Stop Event

1×	iter limit
1×	saturated

Counts

120 → 112

Calls

Call 1

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

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

rewrite56.0ms (2%)

Memory

12.1MiB live, 92.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

106×	`lower-*.f32`
102×	`lower-*.f64`
96×	`lower-/.f64`
96×	`lower-/.f32`
74×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	94
0	34	65
1	99	30
0	742	30

Stop Event

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

Counts

13 → 51

Calls

Call 1

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

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

eval19.0ms (0.7%)

Memory: 6.6MiB live, 43.3MiB allocated
Compiler: Compiled 3 007 to 289 computations (90.4% saved)

prune13.0ms (0.5%)

Memory

-5.5MiB live, 32.7MiB allocated

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	207	3	210
Fresh	0	0	0
Picked	1	2	3
Done	0	4	4
Total	208	9	217

Accuracy

100.0%

Counts

217 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	41.8%	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (*.f64 (sqrt.f64 x) (sqrt.f64 x))))
▶	41.8%	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (fabs.f64 x)))
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	7.2%	(sqrt.f64 (+.f64 x x))
✓	59.3%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	99.2%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
▶	3.9%	#s(literal 0 binary64)

Compiler

Compiled 74 to 47 computations (36.5% saved)

simplify602.0ms (21.2%)

Memory

-0.6MiB live, 1 002.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	64	(fma.f64 x x #s(literal 0 binary64))
✓	cost-diff	320	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (*.f64 (sqrt.f64 x) (sqrt.f64 x))))
✓	cost-diff	1600	(*.f64 (sqrt.f64 x) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	64	(fma.f64 x x #s(literal 0 binary64))
✓	cost-diff	128	(fabs.f64 x)
✓	cost-diff	320	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (fabs.f64 x)))

Rules

28 308×	`lower-fma.f32`
28 306×	`lower-fma.f64`
5 194×	`lower-*.f32`
5 188×	`lower-*.f64`
2 830×	`lower-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	124
0	25	103
1	44	83
2	98	83
3	215	79
4	250	79
5	303	79
6	468	79
7	1184	79
8	2514	79
9	2889	79
10	3324	79
11	3979	79
12	4848	79
13	5986	79
14	6357	79
0	8223	79

Stop Event

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

Calls

Call 1

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

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

localize67.0ms (2.4%)

Memory

-13.6MiB live, 83.7MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.4%	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (*.f64 (sqrt.f64 x) (sqrt.f64 x))))
✓	accuracy	99.2%	(*.f64 (sqrt.f64 x) (sqrt.f64 x))
✓	accuracy	73.8%	(/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
✓	accuracy	67.7%	(sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)))
✓	accuracy	99.9%	(*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))
✓	accuracy	99.4%	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (fabs.f64 x)))
✓	accuracy	73.8%	(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (fabs.f64 x))
✓	accuracy	67.7%	(sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)))

Samples

46.0ms

256×

valid

Compiler

Compiled 136 to 16 computations (88.2% saved)

Precisions

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

ival-mult: 6.0ms (36.2% of total)

ival-sqrt: 4.0ms (24.1% of total)

ival-div: 3.0ms (18.1% of total)

ival-add: 2.0ms (12.1% of total)

ival-fabs: 1.0ms (6% of total)

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

exact: 0.0ms (0% of total)

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

series17.0ms (0.6%)

Memory

-24.7MiB live, 13.1MiB allocated

Counts

10 → 120

Calls

Call 1

Inputs
#<alt (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (fabs.f64 x)))>
#<alt (fabs.f64 x)>
#<alt (fma.f64 x x #s(literal 0 binary64))>
#<alt (sqrt.f64 x)>
#<alt (*.f64 (sqrt.f64 x) (sqrt.f64 x))>
#<alt (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (*.f64 (sqrt.f64 x) (sqrt.f64 x))))>
#<alt (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)))>
#<alt (/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (fabs.f64 x))>
#<alt (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))>
#<alt (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (.f64 (sqrt.f64 x) (sqrt.f64 x)))>

Outputs
#<alt (/ (* (pow x 2) (sqrt 2)) (fabs x))>
#<alt (/ (* (pow x 2) (sqrt 2)) (fabs x))>
#<alt (/ (* (pow x 2) (sqrt 2)) (fabs x))>
#<alt (/ (* (pow x 2) (sqrt 2)) (fabs x))>
#<alt (/ (* (pow x 2) (sqrt 2)) (fabs x))>
#<alt (/ (* (pow x 2) (sqrt 2)) (fabs x))>
#<alt (/ (* (pow x 2) (sqrt 2)) (fabs x))>
#<alt (/ (* (pow x 2) (sqrt 2)) (fabs x))>
#<alt (/ (* (pow x 2) (* (sqrt -2) (sqrt -1))) (fabs x))>
#<alt (/ (* (pow x 2) (* (sqrt -2) (sqrt -1))) (fabs x))>
#<alt (/ (* (pow x 2) (* (sqrt -2) (sqrt -1))) (fabs x))>
#<alt (/ (* (pow x 2) (* (sqrt -2) (sqrt -1))) (fabs x))>
#<alt (fabs x)>
#<alt (fabs x)>
#<alt (fabs x)>
#<alt (fabs x)>
#<alt (fabs x)>
#<alt (fabs x)>
#<alt (fabs x)>
#<alt (fabs x)>
#<alt (fabs x)>
#<alt (fabs x)>
#<alt (fabs x)>
#<alt (fabs x)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt (* -1 (* x (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (pow (sqrt -1) 2)))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (/ (* x (sqrt -2)) (sqrt -1)))>
#<alt (* -1 (/ (* x (sqrt -2)) (sqrt -1)))>
#<alt (* -1 (/ (* x (sqrt -2)) (sqrt -1)))>
#<alt (* -1 (/ (* x (sqrt -2)) (sqrt -1)))>
#<alt (* (sqrt (pow x 3)) (sqrt 2))>
#<alt (* (sqrt (pow x 3)) (sqrt 2))>
#<alt (* (sqrt (pow x 3)) (sqrt 2))>
#<alt (* (sqrt (pow x 3)) (sqrt 2))>
#<alt (* (sqrt (pow x 3)) (sqrt 2))>
#<alt (* (sqrt (pow x 3)) (sqrt 2))>
#<alt (* (sqrt (pow x 3)) (sqrt 2))>
#<alt (* (sqrt (pow x 3)) (sqrt 2))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (pow x 3)) (/ (sqrt 2) (fabs x)))>
#<alt (* (sqrt (pow x 3)) (/ (sqrt 2) (fabs x)))>
#<alt (* (sqrt (pow x 3)) (/ (sqrt 2) (fabs x)))>
#<alt (* (sqrt (pow x 3)) (/ (sqrt 2) (fabs x)))>
#<alt (* (sqrt (pow x 3)) (/ (sqrt 2) (fabs x)))>
#<alt (* (sqrt (pow x 3)) (/ (sqrt 2) (fabs x)))>
#<alt (* (sqrt (pow x 3)) (/ (sqrt 2) (fabs x)))>
#<alt (* (sqrt (pow x 3)) (/ (sqrt 2) (fabs x)))>
#<alt (* (sqrt (pow x 3)) (/ (* (sqrt -2) (sqrt -1)) (fabs x)))>
#<alt (* (sqrt (pow x 3)) (/ (* (sqrt -2) (sqrt -1)) (fabs x)))>
#<alt (* (sqrt (pow x 3)) (/ (* (sqrt -2) (sqrt -1)) (fabs x)))>
#<alt (* (sqrt (pow x 3)) (/ (* (sqrt -2) (sqrt -1)) (fabs x)))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* -1 (* (sqrt x) (/ (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (/ (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (/ (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (/ (sqrt -2) (sqrt -1))))>

Calls

30 calls:

Time	Variable		Point	Expression
8.0ms	x	@	-inf	(/ (sqrt (* (+ (* x x) 0) (+ x x))) (fabs x))
2.0ms	x	@	0	(/ (sqrt (* (+ (* x x) 0) (+ x x))) (fabs x))
1.0ms	x	@	-inf	(* (sqrt x) (/ (sqrt (* (+ (* x x) 0) (+ x x))) (fabs x)))
1.0ms	x	@	-inf	(/ (sqrt (* (+ (* x x) 0) (+ x x))) (* (sqrt x) (sqrt x)))
1.0ms	x	@	-inf	(* (sqrt x) (/ (sqrt (* (+ (* x x) 0) (+ x x))) (* (sqrt x) (sqrt x))))

simplify175.0ms (6.2%)

Memory

27.7MiB live, 259.0MiB allocated

Algorithm

1×	egg-herbie

Rules

2 572×	`lower-*.f64`
2 572×	`lower-*.f32`
2 260×	`lower-fma.f64`
2 260×	`lower-fma.f32`
2 238×	`lower-/.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	644
1	84	644
2	209	644
3	397	644
4	1649	636
5	4790	636
6	6987	636
0	8286	636

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 112

Calls

Call 1

Inputs
(/ (* (pow x 2) (sqrt 2)) (fabs x))
(/ (* (pow x 2) (sqrt 2)) (fabs x))
(/ (* (pow x 2) (sqrt 2)) (fabs x))
(/ (* (pow x 2) (sqrt 2)) (fabs x))
(/ (* (pow x 2) (sqrt 2)) (fabs x))
(/ (* (pow x 2) (sqrt 2)) (fabs x))
(/ (* (pow x 2) (sqrt 2)) (fabs x))
(/ (* (pow x 2) (sqrt 2)) (fabs x))
(/ (* (pow x 2) (* (sqrt -2) (sqrt -1))) (fabs x))
(/ (* (pow x 2) (* (sqrt -2) (sqrt -1))) (fabs x))
(/ (* (pow x 2) (* (sqrt -2) (sqrt -1))) (fabs x))
(/ (* (pow x 2) (* (sqrt -2) (sqrt -1))) (fabs x))
(fabs x)
(fabs x)
(fabs x)
(fabs x)
(fabs x)
(fabs x)
(fabs x)
(fabs x)
(fabs x)
(fabs x)
(fabs x)
(fabs x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
x
x
x
x
x
x
x
x
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (pow (sqrt -1) 2)))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (/ (* x (sqrt -2)) (sqrt -1)))
(* -1 (/ (* x (sqrt -2)) (sqrt -1)))
(* -1 (/ (* x (sqrt -2)) (sqrt -1)))
(* -1 (/ (* x (sqrt -2)) (sqrt -1)))
(* (sqrt (pow x 3)) (sqrt 2))
(* (sqrt (pow x 3)) (sqrt 2))
(* (sqrt (pow x 3)) (sqrt 2))
(* (sqrt (pow x 3)) (sqrt 2))
(* (sqrt (pow x 3)) (sqrt 2))
(* (sqrt (pow x 3)) (sqrt 2))
(* (sqrt (pow x 3)) (sqrt 2))
(* (sqrt (pow x 3)) (sqrt 2))
(* (sqrt (pow x 3)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (pow x 3)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (pow x 3)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (pow x 3)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (pow x 3)) (/ (sqrt 2) (fabs x)))
(* (sqrt (pow x 3)) (/ (sqrt 2) (fabs x)))
(* (sqrt (pow x 3)) (/ (sqrt 2) (fabs x)))
(* (sqrt (pow x 3)) (/ (sqrt 2) (fabs x)))
(* (sqrt (pow x 3)) (/ (sqrt 2) (fabs x)))
(* (sqrt (pow x 3)) (/ (sqrt 2) (fabs x)))
(* (sqrt (pow x 3)) (/ (sqrt 2) (fabs x)))
(* (sqrt (pow x 3)) (/ (sqrt 2) (fabs x)))
(* (sqrt (pow x 3)) (/ (* (sqrt -2) (sqrt -1)) (fabs x)))
(* (sqrt (pow x 3)) (/ (* (sqrt -2) (sqrt -1)) (fabs x)))
(* (sqrt (pow x 3)) (/ (* (sqrt -2) (sqrt -1)) (fabs x)))
(* (sqrt (pow x 3)) (/ (* (sqrt -2) (sqrt -1)) (fabs x)))
(* 2 (pow x 3))
(* 2 (pow x 3))
(* 2 (pow x 3))
(* 2 (pow x 3))
(* 2 (pow x 3))
(* 2 (pow x 3))
(* 2 (pow x 3))
(* 2 (pow x 3))
(* 2 (pow x 3))
(* 2 (pow x 3))
(* 2 (pow x 3))
(* 2 (pow x 3))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* -1 (* (sqrt x) (/ (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (/ (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (/ (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (/ (sqrt -2) (sqrt -1))))

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

rewrite134.0ms (4.7%)

Memory

-6.7MiB live, 223.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 424×	`lower-fma.f32`
2 422×	`lower-fma.f64`
1 662×	`lower-*.f32`
1 660×	`lower-*.f64`
1 036×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	90
0	25	81
1	90	13
2	718	13
3	4568	13
0	8196	13

Stop Event

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

Counts

10 → 361

Calls

Call 1

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

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

eval102.0ms (3.6%)

Memory: 33.8MiB live, 217.5MiB allocated
Compiler: Compiled 18 720 to 1 766 computations (90.6% saved)

prune78.0ms (2.8%)

Memory

6.8MiB live, 209.8MiB allocated

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	830	2	832
Fresh	0	0	0
Picked	2	1	3
Done	0	6	6
Total	832	9	841

Accuracy

100.0%

Counts

841 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
	41.8%	(.f64 (/.f64 x (sqrt.f64 x)) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (fabs.f64 x)))
	41.8%	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) #s(approx (* (sqrt x) (sqrt x)) x)))
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	7.2%	(sqrt.f64 (+.f64 x x))
✓	59.3%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	99.2%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
✓	3.9%	#s(literal 0 binary64)

Compiler

Compiled 195 to 83 computations (57.4% saved)

regimes19.0ms (0.7%)

Memory

-26.4MiB live, 52.4MiB allocated

Counts

13 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

5.0ms	x
5.0ms	(*.f64 x x)
4.0ms	(+.f64 (.f64 x x) (.f64 x x))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Results

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

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes16.0ms (0.6%)

Memory

0.3MiB live, 38.9MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

4 calls:

5.0ms	x
3.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
3.0ms	(*.f64 x x)
3.0ms	(+.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 23 to 10 computations (56.5% saved)

regimes9.0ms (0.3%)

Memory

19.9MiB live, 19.9MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes8.0ms (0.3%)

Memory

-21.4MiB live, 18.6MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	x
1.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
1.0ms	(*.f64 x x)
1.0ms	(+.f64 (.f64 x x) (.f64 x x))

Results

Accuracy	Segments	Branch
7.2%	1	`x`
7.2%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
7.2%	1	`(+.f64 (.f64 x x) (.f64 x x))`
7.2%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes5.0ms (0.2%)

Memory

17.2MiB live, 17.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
3.9%	1	`x`
3.9%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
3.9%	1	`(+.f64 (.f64 x x) (.f64 x x))`
3.9%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify5.0ms (0.2%)

Memory

13.7MiB live, 13.7MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	16	28

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness122.0ms (4.3%)

Memory

-21.1MiB live, 154.3MiB allocated

Rules

106×	`lower-*.f32`
102×	`lower-*.f64`
98×	`lower-*.f32`
96×	`lower-/.f64`
96×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	18
0	7	14
1	23	10
0	160	9
0	15	44
0	23	38
1	51	34
0	255	34
0	21	94
0	34	65
1	99	30
0	742	30
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

Stop Event

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

Compiler

Compiled 110 to 54 computations (50.9% saved)

preprocess106.0ms (3.7%)

Memory: -4.6MiB live, 71.9MiB allocated
Remove: (abs x)
Compiler: Compiled 66 to 32 computations (51.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

Iter	Nodes	Cost
0	4	18
0	7	14
1	23	10
0	160	9
0	15	44
0	23	38
1	51	34
0	255	34
0	21	94
0	34	65
1	99	30
0	742	30
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

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

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

Iter	Nodes	Cost
0	4	18
0	7	14
1	23	10
0	160	9
0	15	44
0	23	38
1	51	34
0	255	34
0	21	94
0	34	65
1	99	30
0	742	30
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

analyze0.0ms (0%)

sample503.0ms (17.8%)

preprocess18.0ms (0.6%)

explain66.0ms (2.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize19.0ms (0.7%)

series3.0ms (0.1%)

simplify7.0ms (0.2%)

rewrite48.0ms (1.7%)

eval8.0ms (0.3%)

prune5.0ms (0.2%)

simplify11.0ms (0.4%)

localize41.0ms (1.5%)

series7.0ms (0.2%)

simplify158.0ms (5.6%)

rewrite35.0ms (1.2%)

eval24.0ms (0.9%)

prune17.0ms (0.6%)

simplify11.0ms (0.4%)

localize96.0ms (3.4%)

series3.0ms (0.1%)

simplify197.0ms (6.9%)

rewrite56.0ms (2%)

eval19.0ms (0.7%)

prune13.0ms (0.5%)

simplify602.0ms (21.2%)

localize67.0ms (2.4%)

series17.0ms (0.6%)

simplify175.0ms (6.2%)

rewrite134.0ms (4.7%)

eval102.0ms (3.6%)

prune78.0ms (2.8%)

regimes19.0ms (0.7%)

regimes16.0ms (0.6%)

regimes9.0ms (0.3%)

regimes8.0ms (0.3%)

regimes5.0ms (0.2%)

simplify5.0ms (0.2%)

soundness122.0ms (4.3%)

preprocess106.0ms (3.7%)

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	3

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

Iter	Nodes	Cost
0	4	18
0	7	14
1	23	10
0	160	9
0	15	44
0	23	38
1	51	34
0	255	34
0	21	94
0	34	65
1	99	30
0	742	30
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148