Metrics for sqrt D (should all be same)

start0.0ms (0%)

Memory: 0.1MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

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)

sample737.0ms (25.4%)

Memory

25.0MiB live, 676.3MiB allocated; 186ms collecting garbage

Samples

499.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 326.0ms

ival-pow2: 167.0ms (51.2% of total)

ival-mult: 86.0ms (26.4% of total)

ival-sqrt: 59.0ms (18.1% of total)

ival-true: 5.0ms (1.5% of total)

exact: 5.0ms (1.5% of total)

ival-assert: 3.0ms (0.9% of total)

adjust: 2.0ms (0.6% of total)

Bogosity

explain140.0ms (4.8%)

Memory

-10.8MiB live, 87.6MiB allocated; 29ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
132	-	3	(-4.5976766556772086e-158)	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
0	-	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))))`	oflow-rescue	76	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	overflow	76
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	76
`sqrt.f64`	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	53	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	underflow	53
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	53

Confusion

	Predicted +	Predicted -
+	129	3
-	0	124

Precision

1.0

Recall

0.9772727272727273

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	129	0	3
-	0	0	124

Precision?

1.0

Recall?

0.9772727272727273

Freqs

test

number	freq
0	127
1	129

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

24.0ms

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 (45.9% of total)

ival-mult: 3.0ms (22.9% of total)

ival-sqrt: 3.0ms (22.9% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

preprocess325.0ms (11.2%)

Memory

-30.6MiB live, 181.1MiB allocated; 50ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	12	13
2	39	13
3	155	13
4	407	13
5	1284	13
6	4857	13
0	5	6
0	8	6
1	13	6
2	34	6
3	106	6
4	358	6
5	1096	6
6	4530	6
0	8083	3

Stop Event

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

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: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.8%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify217.0ms (7.5%)

Memory

7.0MiB live, 150.8MiB allocated; 17ms collecting garbage

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	34	16
3	106	16
4	358	16
5	1096	16
6	4530	16
0	8083	13

Stop Event

1×	iter limit
1×	node limit
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

localize16.0ms (0.6%)

Memory

12.6MiB live, 12.6MiB allocated; 0ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(pow.f64 x #s(literal 2 binary64))
accuracy	0.0078125	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
accuracy	30.208176384583858	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Samples

11.0ms

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 (48.4% of total)

ival-sqrt: 2.0ms (32.2% of total)

ival-mult: 1.0ms (16.1% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

4.2MiB live, 4.2MiB allocated; 0ms collecting garbage

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
#s(approx (sqrt (* 2 (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* 2 (pow x 2)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (pow x 2) #s(hole binary64 (pow x 2)))
#s(approx (sqrt (* 2 (pow x 2))) #s(hole binary64 (* -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))

simplify147.0ms (5.1%)

Memory

9.4MiB live, 96.4MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	41
1	23	41
2	55	41
3	130	41
4	411	41
5	1319	41
6	4910	41
0	8131	35

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 4

Calls

Call 1

Inputs
#s(approx (sqrt (* 2 (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* 2 (pow x 2)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (pow x 2) #s(hole binary64 (pow x 2)))
#s(approx (sqrt (* 2 (pow x 2))) #s(hole binary64 (* -1 (* x (sqrt 2)))))

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

rewrite41.0ms (1.4%)

Memory

-42.3MiB live, 61.6MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	24	12
0	105	11

Stop Event

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

Counts

3 → 39

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

eval4.0ms (0.1%)

Memory: 8.5MiB live, 8.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 382 to 108 computations (71.7% saved)

prune2.0ms (0.1%)

Memory

4.7MiB live, 4.7MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	39	4	43
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	4	44

Accuracy

100.0%

Counts

44 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	49.5%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
▶	52.8%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	52.0%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 25 to 20 computations (20% saved)

simplify170.0ms (5.8%)

Memory

-4.7MiB live, 132.0MiB allocated; 15ms collecting garbage

Localize:

Found 10 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	50
0	24	44
1	38	44
2	89	44
3	206	44
4	551	44
5	1408	44
6	5141	44
0	8107	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) (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 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
x
(+.f64 x x)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
(hypot.f64 x x)
x

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

localize68.0ms (2.3%)

Memory

3.7MiB live, 56.8MiB allocated; 7ms collecting garbage

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(hypot.f64 x x)
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.4453125	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
accuracy	0.0	(+.f64 x x)
accuracy	0.0	(*.f64 x (+.f64 x x))
accuracy	30.208176384583858	(sqrt.f64 (*.f64 x (+.f64 x x)))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.0	(neg.f64 x)
accuracy	0.4453125	(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
accuracy	30.520861866982123	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Samples

28.0ms

256×

valid

Compiler

Compiled 51 to 15 computations (70.6% saved)

Precisions

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

ival-mult: 6.0ms (30.7% of total)

ival-sqrt: 5.0ms (25.6% of total)

ival-hypot: 4.0ms (20.4% of total)

ival-pow2: 3.0ms (15.3% of total)

ival-add: 1.0ms (5.1% of total)

ival-neg: 1.0ms (5.1% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.2%)

Memory

7.9MiB live, 7.9MiB allocated; 0ms collecting garbage

Counts

9 → 11

Calls

Call 1

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

Outputs
#s(approx (sqrt (* 2 (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (neg x) (sqrt 2)) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (* x (+ x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* x (+ x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (* (sqrt 2) x) #s(hole binary64 (* x (sqrt 2))))
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (sqrt (* 2 (pow x 2))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (sqrt (* x (+ x x))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* -1 (* x (sqrt 2)))))

Calls

3 calls:

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

Time

Variable

Point

Expression

2.0ms

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

2.0ms

inf

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

2.0ms

-inf

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

simplify255.0ms (8.8%)

Memory

-12.3MiB live, 177.4MiB allocated; 31ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	112
1	51	112
2	116	112
3	277	112
4	580	112
5	1437	112
6	5726	112
0	8067	94

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 11

Calls

Call 1

Inputs
#s(approx (sqrt (* 2 (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (neg x) (sqrt 2)) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (* x (+ x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* x (+ x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (* (sqrt 2) x) #s(hole binary64 (* x (sqrt 2))))
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (sqrt (* 2 (pow x 2))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (sqrt (* x (+ x x))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* -1 (* x (sqrt 2)))))

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

rewrite56.0ms (1.9%)

Memory

2.3MiB live, 47.0MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	42
0	24	30
1	70	21
0	378	21

Stop Event

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

Counts

9 → 57

Calls

Call 1

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

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

eval3.0ms (0.1%)

Memory: 4.5MiB live, 4.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 449 to 104 computations (76.8% saved)

prune3.0ms (0.1%)

Memory

5.3MiB live, 5.3MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	37	6	43

Accuracy

100.0%

Counts

43 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	49.5%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
▶	49.4%	(.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
✓	52.8%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	5.2%	(sqrt.f64 #s(literal 2 binary64))
✓	52.0%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 34 to 30 computations (11.8% saved)

simplify213.0ms (7.3%)

Memory

5.9MiB live, 189.1MiB allocated; 35ms collecting garbage

Localize:

Found 5 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	24
0	13	19
1	23	18
2	45	18
3	113	18
4	474	18
5	3527	18
0	8378	18

Stop Event

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

Calls

Call 1

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

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

localize23.0ms (0.8%)

Memory

15.1MiB live, 15.1MiB allocated; 0ms collecting garbage

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
accuracy	0.0	(log.f64 #s(literal 2 binary64))
accuracy	0.4453125	(.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
accuracy	1.0	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))

Samples

17.0ms

256×

valid

Compiler

Compiled 26 to 10 computations (61.5% saved)

Precisions

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

ival-mult: 3.0ms (29.3% of total)

ival-log: 2.0ms (19.5% of total)

ival-exp: 2.0ms (19.5% of total)

ival-sqrt: 2.0ms (19.5% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

Outputs
#s(approx (* (exp (* (log 2) 1/2)) x) #s(hole binary64 (* x (sqrt 2))))

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

-inf

((sqrt 2) (exp (* (log 2) 1/2)) (* (exp (* (log 2) 1/2)) x) (* (log 2) 1/2) (log 2))

0.0ms

((sqrt 2) (exp (* (log 2) 1/2)) (* (exp (* (log 2) 1/2)) x) (* (log 2) 1/2) (log 2))

0.0ms

inf

((sqrt 2) (exp (* (log 2) 1/2)) (* (exp (* (log 2) 1/2)) x) (* (log 2) 1/2) (log 2))

simplify187.0ms (6.4%)

Memory

-1.2MiB live, 228.2MiB allocated; 32ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	10
1	21	9
2	44	9
3	110	9
4	471	9
5	3501	9
0	8338	9

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (* (exp (* (log 2) 1/2)) x) #s(hole binary64 (* x (sqrt 2))))

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

rewrite28.0ms (1%)

Memory

7.2MiB live, 50.4MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	20
0	13	14
1	23	13
0	74	13

Stop Event

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

Counts

5 → 28

Calls

Call 1

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

eval2.0ms (0.1%)

Memory: 4.9MiB live, 4.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 207 to 54 computations (73.9% saved)

prune3.0ms (0.1%)

Memory

6.4MiB live, 6.4MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	20	0	20
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	20	6	26

Accuracy

100.0%

Counts

26 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	49.5%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	49.4%	(.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
✓	52.8%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	5.2%	(sqrt.f64 #s(literal 2 binary64))
✓	52.0%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 74 to 53 computations (28.4% saved)

regimes28.0ms (1%)

Memory

-30.6MiB live, 24.7MiB allocated; 20ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

20.0ms	(pow.f64 x #s(literal 2 binary64))
3.0ms	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)))

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)

regimes7.0ms (0.3%)

Memory

16.0MiB live, 16.0MiB allocated; 0ms collecting garbage

Counts

4 → 2

Calls

Call 1

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

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

4 calls:

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

Results

Accuracy	Segments	Branch
76.5%	3	`(pow.f64 x #s(literal 2 binary64))`
76.5%	3	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
76.5%	3	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
99.3%	2	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes5.0ms (0.2%)

Memory

12.3MiB live, 12.3MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

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

Outputs
(sqrt.f64 #s(literal 2 binary64))
(*.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
49.5%	1	`(pow.f64 x #s(literal 2 binary64))`
49.5%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
49.5%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
51.3%	2	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes8.0ms (0.3%)

Memory

-33.5MiB live, 11.2MiB allocated; 8ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

4.0ms	(pow.f64 x #s(literal 2 binary64))
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)))

Results

Accuracy	Segments	Branch
5.2%	1	`(pow.f64 x #s(literal 2 binary64))`
5.2%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
5.2%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
5.2%	1	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

bsearch13.0ms (0.4%)

Memory

21.2MiB live, 21.2MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	-1.3700854308635707e-306	1.3901452499748658e-305

Samples

6.0ms

144×

valid

Compiler

Compiled 153 to 153 computations (0% saved)

Precisions

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

ival-pow2: 2.0ms (57.1% of total)

ival-mult: 1.0ms (28.5% of total)

ival-sqrt: 1.0ms (28.5% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

bsearch13.0ms (0.4%)

Memory

-19.0MiB live, 27.3MiB allocated; 4ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	-6.659521666114716e-203	-9.827286392257744e-207

Samples

5.0ms

128×

valid

Compiler

Compiled 57 to 81 computations (-42.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-mult: 1.0ms (31.9% of total)

ival-sqrt: 1.0ms (31.9% of total)

ival-pow2: 1.0ms (31.9% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

simplify52.0ms (1.8%)

Memory

17.1MiB live, 63.7MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	35
1	29	35
2	54	35
3	129	35
4	397	35
5	2230	35
6	7380	35

Stop Event

1×	node limit

Calls

Call 1

Inputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 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))
(if (<=.f64 x #s(literal -7229475734293037/180736893357325919804742965901096183254486650358500961579737723575212405143116703993975930943694719806137463391890175780999890999416217020648099397663164550811570949854893831716648452639533025774320471006645409943407034368 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 #s(literal 2 binary64))

Outputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 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))
(if (<=.f64 x #s(literal -7229475734293037/180736893357325919804742965901096183254486650358500961579737723575212405143116703993975930943694719806137463391890175780999890999416217020648099397663164550811570949854893831716648452639533025774320471006645409943407034368 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 #s(literal 2 binary64))

derivations42.0ms (1.4%)

Memory

26.5MiB live, 26.5MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 35 to 18 computations (48.6% saved)

preprocess84.0ms (2.9%)

Memory: -34.3MiB live, 65.9MiB allocated; 38ms collecting garbage
Compiler: Compiled 82 to 46 computations (43.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze0.0ms (0%)

sample737.0ms (25.4%)

explain140.0ms (4.8%)

preprocess325.0ms (11.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify217.0ms (7.5%)

localize16.0ms (0.6%)

series3.0ms (0.1%)

simplify147.0ms (5.1%)

rewrite41.0ms (1.4%)

eval4.0ms (0.1%)

prune2.0ms (0.1%)

simplify170.0ms (5.8%)

localize68.0ms (2.3%)

series7.0ms (0.2%)

simplify255.0ms (8.8%)

rewrite56.0ms (1.9%)

eval3.0ms (0.1%)

prune3.0ms (0.1%)

simplify213.0ms (7.3%)

localize23.0ms (0.8%)

series1.0ms (0%)

simplify187.0ms (6.4%)

rewrite28.0ms (1%)

eval2.0ms (0.1%)

prune3.0ms (0.1%)

regimes28.0ms (1%)

regimes7.0ms (0.3%)

regimes5.0ms (0.2%)

regimes8.0ms (0.3%)

bsearch13.0ms (0.4%)

bsearch13.0ms (0.4%)

simplify52.0ms (1.8%)

derivations42.0ms (1.4%)

preprocess84.0ms (2.9%)

end0.0ms (0%)

Profiling