Metrics for sqrt D (should all be same)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB 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 8 to 7 computations (12.5% saved)

sample629.0ms (34%)

Memory

12.3MiB live, 629.2MiB allocated

Samples

412.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 208.0ms

ival-pow2: 91.0ms (43.8% of total)

ival-mult: 53.0ms (25.5% of total)

ival-sqrt: 52.0ms (25% of total)

ival-true: 5.0ms (2.4% of total)

exact: 4.0ms (1.9% of total)

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

Bogosity

explain65.0ms (3.5%)

Memory

4.4MiB live, 106.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
120	-	-	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
0	-	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	61	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	underflow	61
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	61
`sqrt.f64`	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	59	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	overflow	59
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	59

Confusion

	Predicted +	Predicted -
+	120	0
-	0	136

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	120	0	0
-	0	0	136

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	136
1	120

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

31.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-pow2: 6.0ms (45.5% of total)

ival-mult: 3.0ms (22.7% of total)

ival-sqrt: 3.0ms (22.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess22.0ms (1.2%)

Memory

-20.2MiB live, 26.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	12	13
2	32	13
3	99	13
4	153	13
5	247	13
6	273	13
7	293	13
0	5	6
0	8	6
1	13	6
2	27	6
3	64	6
4	132	6
5	204	6
6	240	6
7	263	6
8	278	6
0	278	3

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0.1%)

Memory

1.8MiB live, 1.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.2%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify7.0ms (0.4%)

Memory

5.3MiB live, 5.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 x #s(literal 2 binary64))
cost-diff	0	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
cost-diff	3	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	13	16
2	27	16
3	64	16
4	132	16
5	204	16
6	240	16
7	263	16
8	278	16
0	278	13

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize17.0ms (0.9%)

Memory

16.3MiB live, 16.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(pow.f64 x #s(literal 2 binary64))
accuracy	0.0	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
accuracy	28.00545372394583	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Samples

12.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-pow2: 3.0ms (47.9% of total)

ival-sqrt: 2.0ms (32% of total)

ival-mult: 1.0ms (16% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.2%)

Memory

3.6MiB live, 3.6MiB allocated

Counts

3 → 4

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2))
1.0ms	x	@	0	((sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2))
1.0ms	x	@	-inf	((sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2))

simplify9.0ms (0.5%)

Memory

11.5MiB live, 11.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	18	17
2	43	17
3	92	17
4	228	17
5	437	17
6	485	17
0	485	17

Stop Event

1×	iter limit
1×	saturated

Counts

4 → 4

Calls

Call 1

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

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

rewrite64.0ms (3.5%)

Memory

-3.7MiB live, 42.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	24	12
2	80	10
0	488	9

Stop Event

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

Counts

3 → 96

Calls

Call 1

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

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

eval10.0ms (0.5%)

Memory: 13.3MiB live, 13.3MiB allocated
Compiler: Compiled 1 024 to 269 computations (73.7% saved)

prune14.0ms (0.8%)

Memory

-35.2MiB live, 10.2MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	5	101

Accuracy

100.0%

Counts

101 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	54.4%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
▶	55.2%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
▶	56.2%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
▶	46.2%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 64 to 54 computations (15.6% saved)

simplify9.0ms (0.5%)

Memory

8.0MiB live, 8.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(*.f64 x #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 (.f64 x x) #s(literal 2 binary64))
cost-diff	3	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(neg.f64 x)
cost-diff	0	(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
cost-diff	0	(hypot.f64 x x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	69
0	31	63
1	47	63
2	89	63
3	157	63
4	234	63
5	275	63
6	303	63
7	318	63
0	318	63

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize59.0ms (3.2%)

Memory

13.4MiB live, 70.0MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x #s(literal 2 binary64))
accuracy	0.0	(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.15234375	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
accuracy	0.0	(.f64 (.f64 x x) #s(literal 2 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	14.939675975725295	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.0	(neg.f64 x)
accuracy	0.26171875	(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
accuracy	34.17639614948672	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.26171875	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
accuracy	0.01171875	(hypot.f64 x x)

Samples

27.0ms	116×	0	invalid
20.0ms	140×	0	valid

Compiler

Compiled 70 to 19 computations (72.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-mult: 10.0ms (40% of total)

ival-sqrt: 7.0ms (28% of total)

ival-hypot: 5.0ms (20% of total)

ival-pow2: 2.0ms (8% of total)

ival-neg: 1.0ms (4% of total)

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

exact: 0.0ms (0% of total)

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

series10.0ms (0.5%)

Memory

-34.5MiB live, 12.4MiB allocated

Counts

13 → 11

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x))
2.0ms	x	@	inf	((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x))
2.0ms	x	@	0	((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x))

Time

Variable

Point

Expression

6.0ms

-inf

((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x))

2.0ms

inf

((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x))

2.0ms

((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x))

simplify282.0ms (15.2%)

Memory

26.2MiB live, 251.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	48
1	56	48
2	145	48
3	307	48
4	636	48
5	989	48
6	1074	48
7	1094	48
8	1094	48
9	1214	48
10	1270	48
11	1270	48
12	1386	48
13	1600	48
14	1936	48
15	2304	48
16	2755	48
17	3624	48
18	5022	48
19	7128	48
0	8052	48

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 11

Calls

Call 1

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

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

rewrite30.0ms (1.6%)

Memory

33.8MiB live, 33.8MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	58
0	31	47
1	76	43
0	301	43

Stop Event

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

Counts

13 → 175

Calls

Call 1

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

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

eval16.0ms (0.9%)

Memory: -24.9MiB live, 21.1MiB allocated
Compiler: Compiled 1 026 to 283 computations (72.4% saved)

prune5.0ms (0.2%)

Memory

9.3MiB live, 9.3MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	110	6	116

Accuracy

100.0%

Counts

116 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	54.4%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	55.2%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	56.2%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	46.2%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
▶	46.3%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (neg.f64 x) (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))

Compiler

Compiled 47 to 39 computations (17% saved)

simplify148.0ms (8%)

Memory

-16.1MiB live, 83.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(+.f64 x x)
cost-diff	0	(sqrt.f64 (+.f64 x x))
cost-diff	0	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
cost-diff	0	(neg.f64 x)
cost-diff	0	(.f64 (neg.f64 x) (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (neg.f64 x) (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
cost-diff	3	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	56
0	25	50
1	42	47
2	83	47
3	197	47
4	578	47
5	3118	47
6	7893	47
0	9293	44

Stop Event

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

Calls

Call 1

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

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

localize40.0ms (2.2%)

Memory

8.9MiB live, 55.1MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x x)
accuracy	0.0	(sqrt.f64 (+.f64 x x))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.15234375	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
accuracy	0.0	(log.f64 #s(literal 2 binary64))
accuracy	0.26171875	(.f64 (neg.f64 x) (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
accuracy	0.546875	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
accuracy	34.17639614948672	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (neg.f64 x) (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))

Samples

17.0ms	140×	0	valid
13.0ms	116×	0	invalid

Compiler

Compiled 49 to 17 computations (65.3% saved)

Precisions

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

ival-mult: 7.0ms (32% of total)

ival-sqrt: 4.0ms (18.3% of total)

ival-log: 3.0ms (13.7% of total)

ival-pow2: 3.0ms (13.7% of total)

ival-exp: 2.0ms (9.2% of total)

ival-add: 1.0ms (4.6% of total)

ival-neg: 1.0ms (4.6% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.2%)

Memory

3.7MiB live, 3.7MiB allocated

Counts

9 → 9

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify78.0ms (4.2%)

Memory

-16.4MiB live, 29.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	40
1	51	40
2	133	40
3	248	40
4	448	40
5	632	40
6	680	40
7	713	40
8	743	40
9	764	40
10	930	40
11	987	40
12	987	40
13	1144	40
14	1272	40
15	1497	40
16	1522	40
0	1522	40

Stop Event

1×	iter limit
1×	saturated

Counts

9 → 9

Calls

Call 1

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

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

rewrite32.0ms (1.7%)

Memory

28.3MiB live, 28.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	48
0	25	41
1	64	34
0	242	30

Stop Event

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

Counts

9 → 62

Calls

Call 1

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

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

eval24.0ms (1.3%)

Memory: -31.5MiB live, 19.4MiB allocated
Compiler: Compiled 864 to 207 computations (76% saved)

prune5.0ms (0.2%)

Memory

7.7MiB live, 7.7MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	70	6	76

Accuracy

100.0%

Counts

76 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	54.4%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	55.2%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	56.2%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	46.2%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
✓	46.3%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (neg.f64 x) (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))

Compiler

Compiled 107 to 70 computations (34.6% saved)

regimes11.0ms (0.6%)

Memory

15.7MiB live, 15.7MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

3.0ms	x
3.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
3.0ms	(pow.f64 x #s(literal 2 binary64))
2.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
100.0%	1	`(pow.f64 x #s(literal 2 binary64))`
100.0%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
100.0%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
100.0%	1	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes10.0ms (0.5%)

Memory

-31.0MiB live, 15.0MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	x
2.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
2.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
2.0ms	(pow.f64 x #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
78.8%	3	`(pow.f64 x #s(literal 2 binary64))`
78.8%	3	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
78.8%	3	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
99.4%	2	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes2.0ms (0.1%)

Memory

4.4MiB live, 4.4MiB allocated

Counts

3 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.2%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes4.0ms (0.2%)

Memory

9.9MiB live, 9.9MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

1.0ms	x
1.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
1.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
1.0ms	(pow.f64 x #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
55.2%	1	`(pow.f64 x #s(literal 2 binary64))`
55.2%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
55.2%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
55.2%	1	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

bsearch13.0ms (0.7%)

Memory

21.7MiB live, 21.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	-5.096500352901269e-304	1.1949215157919546e-306

Samples

6.0ms

144×

valid

Compiler

Compiled 180 to 162 computations (10% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-pow2: 2.0ms (56.5% of total)

ival-mult: 1.0ms (28.2% of total)

ival-sqrt: 1.0ms (28.2% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0.1%)

Memory

2.4MiB live, 2.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-5.096500352901269e-304	1.1949215157919546e-306

Compiler

Compiled 153 to 153 computations (0% saved)

simplify49.0ms (2.6%)

Memory

-18.3MiB live, 70.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	50
1	31	50
2	49	50
3	93	50
4	171	50
5	265	50
6	463	50
7	2134	50
8	3822	50

Stop Event

1×	node limit

Calls

Call 1

Inputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -20240225330731/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)))
(if (<=.f64 x #s(literal -20240225330731/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Outputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -20240225330731/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)))
(if (<=.f64 x #s(literal -20240225330731/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

soundness149.0ms (8.1%)

Memory

-10.8MiB live, 136.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	24	12
2	80	10
0	488	9
0	8	17
1	18	17
2	43	17
3	92	17
4	228	17
5	437	17
6	485	17
0	485	17
0	18	58
0	31	47
1	76	43
0	301	43

Stop Event

1×	done
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit
1×	iter limit
1×	saturated
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Compiler

Compiled 116 to 68 computations (41.4% saved)

preprocess26.0ms (1.4%)

Memory: 32.9MiB live, 32.9MiB allocated
Compiler: Compiled 112 to 50 computations (55.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	7	15
1	12	13
2	32	13
3	99	13
4	153	13
5	247	13
6	273	13
7	293	13
0	5	6
0	8	6
1	13	6
2	27	6
3	64	6
4	132	6
5	204	6
6	240	6
7	263	6
8	278	6
0	278	3

Iter	Nodes	Cost
0	5	14
0	8	14
1	24	12
2	80	10
0	488	9
0	8	17
1	18	17
2	43	17
3	92	17
4	228	17
5	437	17
6	485	17
0	485	17
0	18	58
0	31	47
1	76	43
0	301	43

Iter	Nodes	Cost
0	7	15
1	12	13
2	32	13
3	99	13
4	153	13
5	247	13
6	273	13
7	293	13
0	5	6
0	8	6
1	13	6
2	27	6
3	64	6
4	132	6
5	204	6
6	240	6
7	263	6
8	278	6
0	278	3

Iter	Nodes	Cost
0	5	14
0	8	14
1	24	12
2	80	10
0	488	9
0	8	17
1	18	17
2	43	17
3	92	17
4	228	17
5	437	17
6	485	17
0	485	17
0	18	58
0	31	47
1	76	43
0	301	43

start0.0ms (0%)

analyze0.0ms (0%)

sample629.0ms (34%)

explain65.0ms (3.5%)

preprocess22.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0.1%)

simplify7.0ms (0.4%)

localize17.0ms (0.9%)

series4.0ms (0.2%)

simplify9.0ms (0.5%)

rewrite64.0ms (3.5%)

eval10.0ms (0.5%)

prune14.0ms (0.8%)

simplify9.0ms (0.5%)

localize59.0ms (3.2%)

series10.0ms (0.5%)

simplify282.0ms (15.2%)

rewrite30.0ms (1.6%)

eval16.0ms (0.9%)

prune5.0ms (0.2%)

simplify148.0ms (8%)

localize40.0ms (2.2%)

series3.0ms (0.2%)

simplify78.0ms (4.2%)

rewrite32.0ms (1.7%)

eval24.0ms (1.3%)

prune5.0ms (0.2%)

regimes11.0ms (0.6%)

regimes10.0ms (0.5%)

regimes2.0ms (0.1%)

regimes4.0ms (0.2%)

bsearch13.0ms (0.7%)

bsearch1.0ms (0.1%)

simplify49.0ms (2.6%)

soundness149.0ms (8.1%)

preprocess26.0ms (1.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	7	15
1	12	13
2	32	13
3	99	13
4	153	13
5	247	13
6	273	13
7	293	13
0	5	6
0	8	6
1	13	6
2	27	6
3	64	6
4	132	6
5	204	6
6	240	6
7	263	6
8	278	6
0	278	3

Iter	Nodes	Cost
0	5	14
0	8	14
1	24	12
2	80	10
0	488	9
0	8	17
1	18	17
2	43	17
3	92	17
4	228	17
5	437	17
6	485	17
0	485	17
0	18	58
0	31	47
1	76	43
0	301	43