Metrics for sqrt C (should all be same)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample769.0ms (10.1%)

Memory

-31.8MiB live, 725.4MiB allocated

Samples

479.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 222.0ms

ival-mult: 136.0ms (61.3% of total)

ival-sqrt: 73.0ms (32.9% of total)

ival-true: 5.0ms (2.3% of total)

exact: 5.0ms (2.3% of total)

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

Bogosity

explain60.0ms (0.8%)

Memory

16.0MiB live, 64.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
119	0	-	4	(-2.487923194383986e-161)	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(*.f64 x x)`
0	1	(1.3538962241845747e-162)	0	-	`(.f64 #s(literal 2 binary64) (.f64 x x))`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	oflow-rescue	59	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	overflow	59
↳	`(*.f64 x x)`	overflow	59
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	uflow-rescue	56	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	underflow	56
↳	`(*.f64 x x)`	underflow	57
`*.f64`	`(.f64 #s(literal 2 binary64) (.f64 x x))`	*nu**	1	0

Confusion

	Predicted +	Predicted -
+	116	3
-	0	137

Precision

1.0

Recall

0.9747899159663865

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	116	0	3
-	0	0	137

Precision?

1.0

Recall?

0.9747899159663865

Freqs

test

number	freq
0	140
1	116

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

22.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 7.0ms (62.8% of total)

ival-sqrt: 3.0ms (26.9% of total)

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

exact: 0.0ms (0% of total)

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

preprocess17.0ms (0.2%)

Memory

22.1MiB live, 22.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	22	13
2	83	13
3	131	13
4	223	13
5	249	13
6	269	13
0	5	6
0	8	6
1	18	6
2	56	6
3	122	6
4	187	6
5	223	6
6	246	6
7	266	6
0	266	3

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	57.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify6.0ms (0.1%)

Memory

6.9MiB live, 6.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	18	16
2	56	16
3	122	16
4	187	16
5	223	16
6	246	16
7	266	16
0	266	13

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize23.0ms (0.3%)

Memory

-25.5MiB live, 19.9MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.015625	(.f64 #s(literal 2 binary64) (.f64 x x))
accuracy	27.281358431095693	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Samples

18.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

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

ival-sqrt: 9.0ms (69.5% of total)

ival-mult: 3.0ms (23.2% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

4.3MiB live, 4.3MiB allocated

Counts

3 → 4

Calls

Call 1

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

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 (* x x))) (* 2 (* x x)) (* x x))
1.0ms	x	@	0	((sqrt (* 2 (* x x))) (* 2 (* x x)) (* x x))
1.0ms	x	@	-inf	((sqrt (* 2 (* x x))) (* 2 (* x x)) (* x x))

simplify8.0ms (0.1%)

Memory

7.8MiB live, 7.8MiB 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)))

rewrite36.0ms (0.5%)

Memory

-9.6MiB live, 36.6MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	13
1	24	13
2	102	5
0	777	5

Stop Event

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

Counts

3 → 15

Calls

Call 1

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

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

eval2.0ms (0%)

Memory: 4.6MiB live, 4.6MiB allocated
Compiler: Compiled 155 to 71 computations (54.2% saved)

prune1.0ms (0%)

Memory

3.6MiB live, 3.6MiB allocated

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	15	3	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	15	4	19

Accuracy

99.6%

Counts

19 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	57.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
✓	57.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
▶	99.3%	#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	3.8%	#s(literal 0 binary64)

Compiler

Compiled 28 to 23 computations (17.9% saved)

simplify12.0ms (0.2%)

Memory

17.8MiB live, 17.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x (sqrt.f64 x))
cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x)))
cost-diff	3	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
cost-diff	4	(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	54
0	21	54
1	40	42
2	104	42
3	248	42
4	422	42
5	504	42
6	544	42
7	578	42
0	578	36

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize68.0ms (0.9%)

Memory

-43.6MiB live, 52.3MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.015625	(.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x)))
accuracy	0.158535009768442	(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))
accuracy	0.19140625	(*.f64 x (sqrt.f64 x))
accuracy	27.281358431095693	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.0	#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
accuracy	0.4453125	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Samples

31.0ms

256×

valid

Compiler

Compiled 51 to 15 computations (70.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-mult: 12.0ms (66% of total)

ival-sqrt: 6.0ms (33% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

9.2MiB live, 9.2MiB allocated

Counts

7 → 9

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	((sqrt (* 2 (* x x))) (* (sqrt 2) x) (sqrt 2) (* (* x (sqrt x)) (sqrt x)) (sqrt (* 2 (* (* x (sqrt x)) (sqrt x)))) (* 2 (* (* x (sqrt x)) (sqrt x))) (* x (sqrt x)))
1.0ms	x	@	inf	((sqrt (* 2 (* x x))) (* (sqrt 2) x) (sqrt 2) (* (* x (sqrt x)) (sqrt x)) (sqrt (* 2 (* (* x (sqrt x)) (sqrt x)))) (* 2 (* (* x (sqrt x)) (sqrt x))) (* x (sqrt x)))
1.0ms	x	@	0	((sqrt (* 2 (* x x))) (* (sqrt 2) x) (sqrt 2) (* (* x (sqrt x)) (sqrt x)) (sqrt (* 2 (* (* x (sqrt x)) (sqrt x)))) (* 2 (* (* x (sqrt x)) (sqrt x))) (* x (sqrt x)))

Time

Variable

Point

Expression

4.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify137.0ms (1.8%)

Memory

34.3MiB live, 79.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	23	41
1	56	41
2	171	41
3	443	41
4	1239	41
5	2642	33
6	3598	33
7	4030	33
8	4382	33
9	4425	33
10	4425	33
11	4425	33
12	5327	33
13	5431	33
14	5431	33
15	5443	33
16	5443	33
17	5932	33
18	6743	33
0	6743	33

Stop Event

1×	iter limit
1×	saturated

Counts

9 → 9

Calls

Call 1

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

Outputs
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(pow x 2)
(*.f64 x x)
(* 2 (pow x 2))
#s(literal 0 binary64)
(sqrt (pow x 3))
(sqrt.f64 (pow.f64 x #s(literal 3 binary64)))
(* -1 (* x (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))
(* -1 (* (pow x 2) (pow (sqrt -1) 2)))
(*.f64 x x)
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) x))
(* -2 (* (pow x 2) (pow (sqrt -1) 2)))
#s(literal 0 binary64)
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(sqrt.f64 (pow.f64 x #s(literal 3 binary64)))

rewrite87.0ms (1.1%)

Memory

-21.2MiB live, 72.0MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	47
0	20	36
1	49	29
2	188	14
0	998	14

Stop Event

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

Counts

7 → 64

Calls

Call 1

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

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

eval8.0ms (0.1%)

Memory: 17.4MiB live, 17.4MiB allocated
Compiler: Compiled 826 to 280 computations (66.1% saved)

prune3.0ms (0%)

Memory

6.0MiB live, 6.0MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	65	7	72

Accuracy

99.9%

Counts

72 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.9%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
✓	57.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
▶	38.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 (.f64 (.f64 x x) x)) (sqrt.f64 x))))
✓	57.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
▶	99.1%	#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x))
✓	99.3%	#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 61 to 50 computations (18% saved)

simplify33.0ms (0.4%)

Memory

-36.6MiB live, 10.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
cost-diff	0	(*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))
cost-diff	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
cost-diff	0	(.f64 (sqrt.f64 (.f64 (*.f64 x x) x)) (sqrt.f64 x))
cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 (.f64 (.f64 x x) x)) (sqrt.f64 x)))
cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 (.f64 (.f64 x x) x)) (sqrt.f64 x))))
cost-diff	2	(.f64 (.f64 x x) x)
cost-diff	0	(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
cost-diff	0	(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x))
cost-diff	3	(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	104
0	34	104
1	54	88
2	128	85
3	248	85
4	411	85
5	527	85
6	616	85
7	660	85
8	680	85
9	690	85
0	690	82

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize51.0ms (0.7%)

Memory

16.0MiB live, 60.2MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0	(sqrt.f64 x)
accuracy	0.015625	(*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))
accuracy	0.4949953125901448	(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
accuracy	27.281358431095693	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
accuracy	0.08203125	(.f64 (.f64 x x) x)
accuracy	0.158535009768442	(.f64 (sqrt.f64 (.f64 (*.f64 x x) x)) (sqrt.f64 x))
accuracy	21.052499528743237	(sqrt.f64 (.f64 (.f64 x x) x))
accuracy	27.281358431095693	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 (.f64 (.f64 x x) x)) (sqrt.f64 x))))
accuracy	0.0	(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
accuracy	0.0	#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x))
accuracy	0.4453125	(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x)
accuracy	1.0	(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))

Samples

40.0ms

256×

valid

Compiler

Compiled 98 to 21 computations (78.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-mult: 10.0ms (34.5% of total)

ival-sqrt: 10.0ms (34.5% of total)

ival-pow: 6.0ms (20.7% of total)

ival-pow2: 2.0ms (6.9% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.1%)

Memory

13.0MiB live, 13.0MiB allocated

Counts

13 → 15

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify129.0ms (1.7%)

Memory

-2.8MiB live, 42.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	65
1	70	62
2	216	61
3	538	61
4	1960	49
5	4778	49
6	5088	49
7	5241	49
8	5329	49
9	5332	49
10	5332	49
11	5332	49
12	6248	49
13	6334	49
14	6334	49
15	6334	49
16	6334	49
17	6766	49
18	7420	49
0	7420	49

Stop Event

1×	iter limit
1×	saturated

Counts

15 → 15

Calls

Call 1

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

Outputs
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* 2 (pow x 2))
#s(literal 0 binary64)
(pow x 2)
(*.f64 x x)
(sqrt x)
(sqrt.f64 x)
(sqrt (pow x 3))
(sqrt.f64 (pow.f64 x #s(literal 3 binary64)))
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (* (sqrt -1) (sqrt 2))))
(.f64 (.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 2 (* (pow x 2) (pow (sqrt -1) 2)))
#s(literal 0 binary64)
(* (pow x 2) (pow (sqrt -1) 2))
(*.f64 x x)
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* 2 (* (pow x 2) (pow (sqrt -1) 4)))
#s(literal 0 binary64)
(* (pow x 2) (pow (sqrt -1) 4))
(*.f64 x x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))

rewrite86.0ms (1.1%)

Memory

-1.7MiB live, 95.6MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	91
0	34	68
1	93	55
2	335	18
3	1932	18
0	9159	18

Stop Event

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

Counts

13 → 170

Calls

Call 1

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

Outputs
(*.f64 (fabs.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)))
(*.f64 (pow.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64))) #s(literal 4 binary64)) (pow.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64))) #s(literal 4 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) #s(literal 1 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)))
(*.f64 (pow.f64 #s(literal 8 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)) (fabs.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 8 binary64) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 #s(literal 16 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 16 binary64) #s(literal 1/16 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(literal 4 binary64))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (exp.f64 #s(literal 1/4 binary64)) (exp.f64 #s(literal 1/4 binary64))) (log.f64 #s(literal 2 binary64)))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) (log.f64 #s(literal 4 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 2 binary64))))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.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 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 #s(literal 4 binary64)))
(pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)) #s(literal 8 binary64))
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(literal 4 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
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#s(approx (sqrt (* 2 (* x x))) x)
x
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(*.f64 (sqrt.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64))) (sqrt.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64))))
(*.f64 (sqrt.f64 (pow.f64 #s(literal 8 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 8 binary64) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 8 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 8 binary64) #s(literal 1/16 binary64)) (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64))))
(*.f64 (pow.f64 #s(literal 8 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)))
(*.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64))) (pow.f64 #s(literal 8 binary64) #s(literal 1/16 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)) (fabs.f64 (pow.f64 #s(literal 8 binary64) #s(literal 1/16 binary64))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)) (sqrt.f64 (pow.f64 #s(literal 8 binary64) #s(literal 1/8 binary64))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)) (pow.f64 (pow.f64 #s(literal 8 binary64) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)) (pow.f64 (pow.f64 #s(literal 8 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 8 binary64) #s(literal 1/16 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(literal 4 binary64))) #s(literal 1/8 binary64))
(pow.f64 (exp.f64 #s(literal 1/8 binary64)) (log.f64 #s(literal 4 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (/.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 2 binary64))))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1 binary64)))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 16 binary64) #s(literal 1/16 binary64))
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)) #s(literal 4 binary64))
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 #s(literal 16 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
(/.f64 (-.f64 (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)) (pow.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (-.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64))))))
(/.f64 (+.f64 (pow.f64 (neg.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64))))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)) (.f64 (neg.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64))))) (sinh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64))))))))
(/.f64 (+.f64 (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 3 binary64)) (pow.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)) (-.f64 (pow.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (cosh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64))))))))
(/.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))) #s(literal 2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 16 binary64) #s(literal 1/16 binary64)))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 16 binary64) #s(literal 1/16 binary64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)) (.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) (sinh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 3 binary64)))) (+.f64 (pow.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)) (.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) (sinh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))))))
(/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64))))))) #s(literal 4 binary64))
(/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64))))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))))) #s(literal 4 binary64))
(/.f64 (fabs.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 3 binary64)))) (fabs.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)) (.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) (sinh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))))))
(/.f64 (hypot.f64 (pow.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3/2 binary64)) (pow.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3/2 binary64))) (sqrt.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) #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 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 3 binary64))) (neg.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)) (.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) (sinh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)) (.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) (sinh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))))))
(/.f64 #s(literal 1 binary64) (-.f64 (neg.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64))))) (sinh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 16 binary64) #s(literal 1/16 binary64)))))
(/.f64 #s(literal 1 binary64) (fabs.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 16 binary64) #s(literal 1/16 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 16 binary64) #s(literal 1/16 binary64))))
(neg.f64 (pow.f64 #s(literal 16 binary64) #s(literal 1/16 binary64)))
(fma.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (cosh.f64 (.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 2 binary64)))) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (sinh.f64 (*.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 2 binary64))))))
(fma.f64 #s(literal 2 binary64) (.f64 (sinh.f64 (.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 2 binary64)))) (cosh.f64 (.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 2 binary64))))) (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))))
(sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))
(-.f64 (/.f64 (pow.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 16 binary64) #s(literal 1/16 binary64)))) (/.f64 (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 16 binary64) #s(literal 1/16 binary64)))))
(fabs.f64 (pow.f64 #s(literal 16 binary64) #s(literal 1/16 binary64)))
(exp.f64 (/.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 1/4 binary64))) (log.f64 #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(+.f64 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (cosh.f64 (.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 2 binary64))))) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (sinh.f64 (.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 2 binary64))))))
(+.f64 (neg.f64 (neg.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))))) (neg.f64 (sinh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64))))))
(+.f64 (/.f64 (pow.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (+.f64 (pow.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)) (.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))))) (/.f64 (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 3 binary64)) (+.f64 (pow.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)) (.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))))))
(+.f64 (sinh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) (neg.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64))))))
(+.f64 (neg.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64))))) (sinh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))))
(+.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))))
(+.f64 (cosh.f64 (.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64)))) (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
x
#s(literal 0 binary64)
x
#s(literal 0 binary64)
x
#s(literal 0 binary64)
x
#s(literal 0 binary64)
x
#s(literal 0 binary64)
x
#s(literal 0 binary64)
x
#s(literal 0 binary64)
x
#s(literal 0 binary64)
x
#s(literal 0 binary64)

eval23.0ms (0.3%)

Memory: -2.2MiB live, 42.8MiB allocated
Compiler: Compiled 4 098 to 774 computations (81.1% saved)

prune4.0ms (0.1%)

Memory

12.3MiB live, 12.3MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	0	0	0
Picked	2	1	3
Done	1	3	4
Total	166	6	172

Accuracy

99.9%

Counts

172 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	57.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
✓	38.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 (.f64 (.f64 x x) x)) (sqrt.f64 x))))
✓	57.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
▶	99.1%	#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x))
✓	99.3%	#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	20.3%	#s(approx (sqrt (* 2 (* x x))) x)

Compiler

Compiled 61 to 47 computations (23% saved)

simplify8.0ms (0.1%)

Memory

12.6MiB live, 12.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	42
0	15	39
1	27	33
2	75	33
3	161	33
4	261	33
5	307	33
6	327	33
7	347	33
0	347	27

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize48.0ms (0.6%)

Memory

-25.3MiB live, 72.1MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.0	#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x))
accuracy	0.4453125	(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x)
accuracy	1.0	(pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64))
accuracy	50.99569926648028	#s(approx (sqrt (* 2 (* x x))) x)

Samples

41.0ms

256×

valid

Compiler

Compiled 34 to 11 computations (67.6% saved)

Precisions

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

ival-pow2: 17.0ms (63.8% of total)

ival-mult: 5.0ms (18.8% of total)

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

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

2.3MiB live, 2.3MiB allocated

Counts

6 → 2

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

-inf

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

0.0ms

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

0.0ms

inf

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

simplify3.0ms (0%)

Memory

4.7MiB live, 4.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	27	9
3	28	9
0	28	9

Stop Event

1×	iter limit
1×	saturated

Counts

2 → 2

Calls

Call 1

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

rewrite44.0ms (0.6%)

Memory

-13.3MiB live, 34.0MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	39
0	15	34
1	41	28
2	161	14
0	1083	14

Stop Event

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

Counts

6 → 67

Calls

Call 1

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

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

eval5.0ms (0.1%)

Memory: 7.4MiB live, 7.4MiB allocated
Compiler: Compiled 802 to 192 computations (76.1% saved)

prune4.0ms (0.1%)

Memory

6.2MiB live, 6.2MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	46	6	52

Accuracy

99.9%

Counts

52 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	57.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
✓	38.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 (.f64 (.f64 x x) x)) (sqrt.f64 x))))
✓	57.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
✓	99.1%	#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x))
✓	99.3%	#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	20.3%	#s(approx (sqrt (* 2 (* x x))) x)

Compiler

Compiled 144 to 84 computations (41.7% saved)

regimes13.0ms (0.2%)

Memory

16.1MiB live, 16.1MiB allocated

Counts

9 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(approx (sqrt (* 2 (* x x))) x)
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 (.f64 (.f64 x x) x)) (sqrt.f64 x))))
#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x))

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
99.3%	1	`(.f64 #s(literal 2 binary64) (.f64 x x))`
99.3%	1	`(*.f64 x x)`

Compiler

Compiled 15 to 12 computations (20% saved)

regimes10.0ms (0.1%)

Memory

-36.2MiB live, 10.0MiB allocated

Counts

2 → 1

Calls

Call 1

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

Outputs
#s(approx (sqrt (* 2 (* x x))) x)

Calls

4 calls:

5.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
1.0ms	x
1.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
20.3%	1	`x`
20.3%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
20.3%	1	`(.f64 #s(literal 2 binary64) (.f64 x x))`
20.3%	1	`(*.f64 x x)`

Compiler

Compiled 15 to 12 computations (20% saved)

regimes5.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB 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 #s(literal 2 binary64) (.f64 x x)))
1.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
3.8%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
3.8%	1	`(.f64 #s(literal 2 binary64) (.f64 x x))`
3.8%	1	`(*.f64 x x)`
3.8%	1	`x`

Compiler

Compiled 15 to 12 computations (20% saved)

simplify41.0ms (0.5%)

Memory

2.1MiB live, 46.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	20	20
2	57	20
3	128	20
4	199	20
5	261	20
6	451	20
7	2047	20
8	3202	20

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness5.9s (76.6%)

Memory

1.3MiB live, 186.7MiB allocated

Iterations

Useful iterations: 2 (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
0	5	14
0	8	13
1	24	13
2	102	5
0	777	5
0	13	47
0	20	36
1	49	29
2	188	14
0	998	14
0	21	91
0	34	68
1	93	55
2	335	18
3	1932	18
0	9159	18

Stop Event

1×	done
1×	iter limit
1×	node limit
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
1×	iter limit
1×	saturated

Compiler

Compiled 46 to 34 computations (26.1% saved)

preprocess19.0ms (0.3%)

Memory: 35.9MiB live, 35.9MiB allocated
Compiler: Compiled 74 to 50 computations (32.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	7	13
1	22	13
2	83	13
3	131	13
4	223	13
5	249	13
6	269	13
0	5	6
0	8	6
1	18	6
2	56	6
3	122	6
4	187	6
5	223	6
6	246	6
7	266	6
0	266	3

Iter	Nodes	Cost
0	21	104
0	34	104
1	54	88
2	128	85
3	248	85
4	411	85
5	527	85
6	616	85
7	660	85
8	680	85
9	690	85
0	690	82

Iter	Nodes	Cost
0	7	13
1	22	13
2	83	13
3	131	13
4	223	13
5	249	13
6	269	13
0	5	6
0	8	6
1	18	6
2	56	6
3	122	6
4	187	6
5	223	6
6	246	6
7	266	6
0	266	3

Iter	Nodes	Cost
0	21	104
0	34	104
1	54	88
2	128	85
3	248	85
4	411	85
5	527	85
6	616	85
7	660	85
8	680	85
9	690	85
0	690	82

start0.0ms (0%)

analyze0.0ms (0%)

sample769.0ms (10.1%)

explain60.0ms (0.8%)

preprocess17.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize23.0ms (0.3%)

series3.0ms (0%)

simplify8.0ms (0.1%)

rewrite36.0ms (0.5%)

eval2.0ms (0%)

prune1.0ms (0%)

simplify12.0ms (0.2%)

localize68.0ms (0.9%)

series6.0ms (0.1%)

simplify137.0ms (1.8%)

rewrite87.0ms (1.1%)

eval8.0ms (0.1%)

prune3.0ms (0%)

simplify33.0ms (0.4%)

localize51.0ms (0.7%)

series7.0ms (0.1%)

simplify129.0ms (1.7%)

rewrite86.0ms (1.1%)

eval23.0ms (0.3%)

prune4.0ms (0.1%)

simplify8.0ms (0.1%)

localize48.0ms (0.6%)

series1.0ms (0%)

simplify3.0ms (0%)

rewrite44.0ms (0.6%)

eval5.0ms (0.1%)

prune4.0ms (0.1%)

regimes13.0ms (0.2%)

regimes10.0ms (0.1%)

regimes5.0ms (0.1%)

simplify41.0ms (0.5%)

soundness5.9s (76.6%)

preprocess19.0ms (0.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	7	13
1	22	13
2	83	13
3	131	13
4	223	13
5	249	13
6	269	13
0	5	6
0	8	6
1	18	6
2	56	6
3	122	6
4	187	6
5	223	6
6	246	6
7	266	6
0	266	3

Iter	Nodes	Cost
0	21	104
0	34	104
1	54	88
2	128	85
3	248	85
4	411	85
5	527	85
6	616	85
7	660	85
8	680	85
9	690	85
0	690	82