Metrics for sqrt D (should all be same)

start0.0ms (0%)

Memory: 0.0MiB 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)

sample510.0ms (54.7%)

Memory

13.1MiB live, 481.3MiB allocated; 49ms collecting garbage

Samples

352.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 204.0ms

ival-pow2: 95.0ms (46.5% of total)

ival-sqrt: 71.0ms (34.8% of total)

ival-mult!: 36.0ms (17.6% of total)

adjust: 2.0ms (1% of total)

Bogosity

explain68.0ms (7.3%)

Memory

-2.3MiB live, 43.7MiB allocated; 4ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
118	-	1	(5.767814215362851e-157)	`(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))))`	uflow-rescue	61	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	underflow	61
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	61
`sqrt.f64`	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	56	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	overflow	56
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	56

Confusion

	Predicted +	Predicted -
+	117	1
-	0	138

Precision

1.0

Recall

0.9915254237288136

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	117	0	1
-	0	0	138

Precision?

1.0

Recall?

0.9915254237288136

Freqs

test

number	freq
0	139
1	117

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-sqrt: 20.0ms (72.6% of total)

ival-pow2: 6.0ms (21.8% of total)

ival-mult!: 2.0ms (7.3% of total)

adjust: 0.0ms (0% of total)

preprocess129.0ms (13.8%)

Memory

-13.4MiB live, 37.1MiB allocated; 60ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	19
2	55	19
3	167	19
4	408	19
5	1304	19
6	5101	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

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

Symmetry

(abs x)

Compiler

Compiled 12 to 10 computations (16.7% saved)

series4.0ms (0.4%)

Memory

4.6MiB live, 4.6MiB allocated; 0ms collecting garbage

Counts

5 → 5

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

Calls

3 calls:

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

rewrite43.0ms (4.7%)

Memory

-1.9MiB live, 48.2MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	61
0	21	60
1	42	54
0	138	49

Stop Event

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

Counts

10 → 46

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

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

eval4.0ms (0.4%)

Memory: 6.0MiB live, 6.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 382 to 109 computations (71.5% saved)

prune2.0ms (0.2%)

Memory

3.1MiB live, 3.1MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	40	3	43
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	3	44

Accuracy

100.0%

Counts

44 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
▶	57.3%	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 13 to 10 computations (23.1% saved)

series3.0ms (0.3%)

Memory

5.0MiB live, 5.0MiB allocated; 0ms collecting garbage

Counts

8 → 8

Calls

Call 1

Inputs
(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)
(hypot.f64 x x)

Outputs
#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 #s(hole binary64 x))
#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 (* 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
1.0ms	x	@	-inf	((sqrt (* x (+ x x))) (* x (+ x x)) x (+ x x) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (+ (* x x) (* x x))))
1.0ms	x	@	inf	((sqrt (* x (+ x x))) (* x (+ x x)) x (+ x x) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (+ (* x x) (* x x))))
1.0ms	x	@	0	((sqrt (* x (+ x x))) (* x (+ x x)) x (+ x x) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (+ (* x x) (* x x))))

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

rewrite66.0ms (7%)

Memory

-2.7MiB live, 42.8MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	97
0	35	91
1	82	62
0	437	62

Stop Event

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

Counts

16 → 56

Calls

Call 1

Inputs
(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)
(hypot.f64 x 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 #s(hole binary64 x))
#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 (* 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
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 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 (*.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)
x
#s(literal 2 binary64)
(*.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 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 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 (*.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)
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 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 (*.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(approx (sqrt (* x (+ x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (* x (+ x x)) #s(literal 2 binary64))
#s(approx x x)
#s(approx (* x (+ x x)) #s(literal 2 binary64))
#s(approx (* (sqrt 2) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (* x (+ x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (* x (+ x x))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (* x (+ x x))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

eval2.0ms (0.2%)

Memory: 4.1MiB live, 4.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 169 to 68 computations (59.8% saved)

prune2.0ms (0.2%)

Memory

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

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	23	5	28

Accuracy

100.0%

Counts

28 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
✓	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	57.3%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	5.3%	(sqrt.f64 #s(approx (* x (+ x x)) #s(literal 2 binary64)))

Compiler

Compiled 26 to 21 computations (19.2% saved)

series3.0ms (0.3%)

Memory

5.0MiB live, 5.0MiB allocated; 0ms collecting garbage

Counts

7 → 6

Calls

Call 1

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

Outputs
#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 (* (sqrt 2) (fabs x)) #s(hole binary64 (* (fabs x) (sqrt 2))))
#s(approx (fabs x) #s(hole binary64 (fabs x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (* 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)) 2 (* (sqrt 2) (fabs x)) (sqrt 2) (fabs x) x)
1.0ms	x	@	inf	((sqrt (* x (+ x x))) (* x (+ x x)) 2 (* (sqrt 2) (fabs x)) (sqrt 2) (fabs x) x)
1.0ms	x	@	0	((sqrt (* x (+ x x))) (* x (+ x x)) 2 (* (sqrt 2) (fabs x)) (sqrt 2) (fabs x) x)

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

rewrite40.0ms (4.3%)

Memory

-9.0MiB live, 36.7MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	80
0	28	73
1	66	39
0	261	39

Stop Event

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

Counts

13 → 34

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (* x (+ x x)) #s(literal 2 binary64)))
#s(approx (* x (+ x x)) #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(sqrt.f64 #s(literal 2 binary64))
(fabs.f64 x)
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 (* (sqrt 2) (fabs x)) #s(hole binary64 (* (fabs x) (sqrt 2))))
#s(approx (fabs x) #s(hole binary64 (fabs x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (* x (+ x x))) #s(hole binary64 (* -1 (* x (sqrt 2)))))

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

eval1.0ms (0.2%)

Memory: 2.2MiB live, 2.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 113 to 41 computations (63.7% saved)

prune2.0ms (0.3%)

Memory

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

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	15	0	15
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	15	5	20

Accuracy

100.0%

Counts

20 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
✓	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	57.3%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	5.3%	(sqrt.f64 #s(approx (* x (+ x x)) #s(literal 2 binary64)))

Compiler

Compiled 58 to 38 computations (34.5% saved)

regimes9.0ms (0.9%)

Memory

13.0MiB live, 13.0MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
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 (0.7%)

Memory

12.1MiB live, 12.0MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.4%	1	`(pow.f64 x #s(literal 2 binary64))`
99.4%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
99.4%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
99.4%	1	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes15.0ms (1.6%)

Memory

-39.2MiB live, 15.8MiB allocated; 5ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

12.0ms	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
5.3%	1	`(pow.f64 x #s(literal 2 binary64))`
5.3%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
5.3%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
5.3%	1	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

derivations6.0ms (0.6%)

Memory

6.1MiB live, 6.1MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 15 to 9 computations (40% saved)

preprocess16.0ms (1.7%)

Memory: 24.0MiB live, 24.0MiB allocated; 0ms collecting garbage
Remove: (abs x)
Compiler: Compiled 72 to 52 computations (27.8% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample510.0ms (54.7%)

explain68.0ms (7.3%)

preprocess129.0ms (13.8%)

series4.0ms (0.4%)

rewrite43.0ms (4.7%)

eval4.0ms (0.4%)

prune2.0ms (0.2%)

series3.0ms (0.3%)

rewrite66.0ms (7%)

eval2.0ms (0.2%)

prune2.0ms (0.2%)

series3.0ms (0.3%)

rewrite40.0ms (4.3%)

eval1.0ms (0.2%)

prune2.0ms (0.3%)

regimes9.0ms (0.9%)

regimes7.0ms (0.7%)

regimes15.0ms (1.6%)

derivations6.0ms (0.6%)

preprocess16.0ms (1.7%)

end0.0ms (0%)

Profiling