Metrics for sqrt A (should all be same)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB 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 10 to 4 computations (60% saved)

sample718.0ms (33.4%)

Memory

36.1MiB live, 962.9MiB allocated; 234ms collecting garbage

Samples

484.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 217.0ms

ival-hypot: 204.0ms (94% of total)

ival-true: 7.0ms (3.2% of total)

ival-assert: 4.0ms (1.8% of total)

adjust: 3.0ms (1.4% of total)

Bogosity

explain71.0ms (3.3%)

Memory

31.7MiB live, 125.0MiB allocated; 7ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
124	-	2	(-1.7018849600979206e-160)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 x x))`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	oflow-rescue	64	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	overflow	64
↳	`(*.f64 x x)`	overflow	128
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	uflow-rescue	58	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	underflow	58
↳	`(*.f64 x x)`	underflow	116

Confusion

	Predicted +	Predicted -
+	122	2
-	0	132

Precision

1.0

Recall

0.9838709677419355

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	122	0	2
-	0	0	132

Precision?

1.0

Recall?

0.9838709677419355

Freqs

test

number	freq
0	134
1	122

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

28.0ms

512×

valid

Compiler

Compiled 50 to 16 computations (68% saved)

Precisions

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

ival-hypot: 9.0ms (53% of total)

ival-mult: 4.0ms (23.5% of total)

ival-add: 2.0ms (11.8% of total)

ival-true: 1.0ms (5.9% of total)

adjust: 0.0ms (0% of total)

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

preprocess224.0ms (10.4%)

Memory

12.4MiB live, 154.8MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	29	19
2	84	19
3	144	19
4	298	19
5	663	19
6	1542	19
7	3518	19
0	4	8
0	7	6
1	17	6
2	54	6
3	135	6
4	264	6
5	612	6
6	1430	6
7	5304	6
0	8068	3

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 8 to 4 computations (50% 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

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.0%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 8 to 4 computations (50% saved)

simplify196.0ms (9.1%)

Memory

-36.6MiB live, 101.5MiB allocated; 21ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	2	(+.f64 (.f64 x x) (.f64 x x))
cost-diff	3	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	19
0	7	15
1	17	15
2	54	15
3	135	15
4	264	15
5	612	15
6	1430	15
7	5304	15
0	8068	12

Stop Event

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

Calls

Call 1

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

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

localize18.0ms (0.8%)

Memory

19.7MiB live, 19.7MiB allocated; 0ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (.f64 x x) (.f64 x x))
accuracy	28.795561539218873	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Samples

13.0ms

256×

valid

Compiler

Compiled 21 to 6 computations (71.4% saved)

Precisions

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

ival-hypot: 5.0ms (64.4% of total)

ival-mult: 2.0ms (25.8% of total)

ival-add: 1.0ms (12.9% of total)

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

adjust: 0.0ms (0% of total)

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

series3.0ms (0.2%)

Memory

3.9MiB live, 3.9MiB allocated; 0ms collecting garbage

Counts

3 → 4

Calls

Call 1

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

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

Calls

3 calls:

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

simplify164.0ms (7.6%)

Memory

10.5MiB live, 99.7MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	34	41
2	94	41
3	230	41
4	474	41
5	1351	41
6	5631	41
0	8212	35

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 4

Calls

Call 1

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

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

rewrite70.0ms (3.2%)

Memory

-13.7MiB live, 44.9MiB allocated; 30ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	18
0	7	14
1	29	10
0	250	9

Stop Event

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

Counts

3 → 107

Calls

Call 1

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

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

eval12.0ms (0.6%)

Memory: 17.5MiB live, 17.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 053 to 257 computations (75.6% saved)

prune7.0ms (0.3%)

Memory

-37.8MiB live, 8.6MiB allocated; 5ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	4	126

Accuracy

100.0%

Counts

126 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	99.5%	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
▶	55.0%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
▶	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify152.0ms (7.1%)

Memory

27.4MiB live, 116.7MiB allocated; 10ms collecting garbage

Localize:

Found 11 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	54
0	25	51
1	41	51
2	89	51
3	214	51
4	437	51
5	1267	51
6	5243	51
0	8025	51

Stop Event

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

Calls

Call 1

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

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

localize54.0ms (2.5%)

Memory

1.3MiB live, 51.6MiB allocated; 9ms collecting garbage

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(hypot.f64 x x)
accuracy	0.0	(*.f64 #s(literal 2 binary64) x)
accuracy	0.0	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.34765625	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
accuracy	0.0	(*.f64 x x)
accuracy	0.00390625	(.f64 (.f64 x x) #s(literal 2 binary64))
accuracy	28.795561539218873	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.0	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
accuracy	0.41796875	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Samples

41.0ms

256×

valid

Compiler

Compiled 61 to 14 computations (77% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-mult: 7.0ms (37% of total)

ival-sqrt: 6.0ms (31.7% of total)

ival-hypot: 5.0ms (26.4% 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)

series7.0ms (0.3%)

Memory

8.4MiB live, 8.4MiB allocated; 0ms collecting garbage

Counts

11 → 14

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x) (sqrt (+ (* x x) (* x x))))
2.0ms	x	@	inf	((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x) (sqrt (+ (* x x) (* x x))))
1.0ms	x	@	0	((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x) (sqrt (+ (* x x) (* x x))))

Time

Variable

Point

Expression

3.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

simplify29.0ms (1.3%)

Memory

-28.0MiB live, 17.4MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	142
1	86	142
2	221	142
0	557	130

Stop Event

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

Counts

14 → 14

Calls

Call 1

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

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

rewrite48.0ms (2.2%)

Memory

37.3MiB live, 37.3MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	47
0	25	37
1	61	32
0	321	32

Stop Event

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

Counts

11 → 79

Calls

Call 1

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

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

eval11.0ms (0.5%)

Memory: -34.5MiB live, 10.9MiB allocated; 4ms collecting garbage
Compiler: Compiled 638 to 194 computations (69.6% saved)

prune3.0ms (0.2%)

Memory

5.9MiB live, 5.9MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	56	5	61

Accuracy

100.0%

Counts

61 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	55.0%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
▶	5.5%	(sqrt.f64 #s(literal 2 binary64))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 31 to 23 computations (25.8% saved)

simplify145.0ms (6.7%)

Memory

-0.5MiB live, 92.4MiB allocated; 12ms collecting garbage

Localize:

Found 5 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	12	20
1	16	20
2	20	20
3	31	20
4	71	20
5	266	20
6	1435	20
7	6835	20
0	8097	20

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

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

localize21.0ms (1%)

Memory

23.3MiB live, 23.3MiB allocated; 0ms collecting garbage

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x x)
accuracy	0.0	(sqrt.f64 (+.f64 x x))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.34765625	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))

Samples

15.0ms

256×

valid

Compiler

Compiled 22 to 9 computations (59.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-sqrt: 5.0ms (58.4% of total)

ival-mult: 2.0ms (23.4% of total)

ival-add: 1.0ms (11.7% 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

3.7MiB live, 3.7MiB allocated; 0ms collecting garbage

Counts

5 → 7

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify19.0ms (0.9%)

Memory

-32.3MiB live, 13.4MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	69
1	56	69
2	139	69
0	333	69

Stop Event

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

Counts

7 → 7

Calls

Call 1

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

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

rewrite24.0ms (1.1%)

Memory

18.8MiB live, 18.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	18
0	12	11
1	31	9
0	159	9

Stop Event

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

Counts

5 → 29

Calls

Call 1

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

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

eval2.0ms (0.1%)

Memory: 2.8MiB live, 2.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 165 to 63 computations (61.8% saved)

prune3.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	19	0	19
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	19	5	24

Accuracy

100.0%

Counts

24 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	55.0%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	5.5%	(sqrt.f64 #s(literal 2 binary64))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 77 to 44 computations (42.9% saved)

regimes9.0ms (0.4%)

Memory

13.8MiB live, 13.8MiB allocated; 0ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

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

Results

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

Compiler

Compiled 19 to 10 computations (47.4% saved)

regimes12.0ms (0.6%)

Memory

-31.2MiB live, 14.7MiB allocated; 3ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

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

Calls

4 calls:

6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	x
2.0ms	(+.f64 (.f64 x x) (.f64 x x))
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.5%	1	`(*.f64 x x)`
99.5%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.5%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.5%	1	`x`

Compiler

Compiled 19 to 10 computations (47.4% saved)

regimes7.0ms (0.3%)

Memory

11.0MiB live, 11.0MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 19 to 10 computations (47.4% saved)

regimes4.0ms (0.2%)

Memory

8.0MiB live, 8.0MiB allocated; 0ms 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:

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

Results

Accuracy	Segments	Branch
5.5%	1	`(*.f64 x x)`
5.5%	1	`(+.f64 (.f64 x x) (.f64 x x))`
5.5%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
5.5%	1	`x`

Compiler

Compiled 19 to 10 computations (47.4% saved)

simplify43.0ms (2%)

Memory

-16.9MiB live, 29.2MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	24	23
2	62	23
3	154	23
4	343	23
5	1581	23
6	5172	23

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations44.0ms (2%)

Memory

33.2MiB live, 33.2MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 25 to 13 computations (48% saved)

preprocess29.0ms (1.3%)

Memory: -18.1MiB live, 30.9MiB allocated; 8ms collecting garbage
Remove: (abs x)
Compiler: Compiled 72 to 38 computations (47.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample718.0ms (33.4%)

explain71.0ms (3.3%)

preprocess224.0ms (10.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify196.0ms (9.1%)

localize18.0ms (0.8%)

series3.0ms (0.2%)

simplify164.0ms (7.6%)

rewrite70.0ms (3.2%)

eval12.0ms (0.6%)

prune7.0ms (0.3%)

simplify152.0ms (7.1%)

localize54.0ms (2.5%)

series7.0ms (0.3%)

simplify29.0ms (1.3%)

rewrite48.0ms (2.2%)

eval11.0ms (0.5%)

prune3.0ms (0.2%)

simplify145.0ms (6.7%)

localize21.0ms (1%)

series3.0ms (0.1%)

simplify19.0ms (0.9%)

rewrite24.0ms (1.1%)

eval2.0ms (0.1%)

prune3.0ms (0.1%)

regimes9.0ms (0.4%)

regimes12.0ms (0.6%)

regimes7.0ms (0.3%)

regimes4.0ms (0.2%)

simplify43.0ms (2%)

derivations44.0ms (2%)

preprocess29.0ms (1.3%)

end0.0ms (0%)

Profiling