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, 0.2MiB 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)

sample563.0ms (61%)

Memory

26.4MiB live, 634.8MiB allocated; 113ms collecting garbage

Samples

365.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 225.0ms

ival-pow2: 106.0ms (47% of total)

ival-sqrt: 60.0ms (26.6% of total)

ival-mult!: 58.0ms (25.7% of total)

adjust: 1.0ms (0.4% of total)

Bogosity

explain60.0ms (6.5%)

Memory

-7.7MiB live, 89.2MiB allocated; 9ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
120	-	3	(4.489789364936543e-162)	`(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	64	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	underflow	64
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	64
`sqrt.f64`	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	53	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	overflow	53
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	53

Confusion

	Predicted +	Predicted -
+	117	3
-	0	136

Precision

1.0

Recall

0.975

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	117	0	3
-	0	0	136

Precision?

1.0

Recall?

0.975

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

22.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-pow2: 6.0ms (50.2% of total)

ival-sqrt: 3.0ms (25.1% of total)

ival-mult!: 2.0ms (16.7% of total)

adjust: 0.0ms (0% of total)

preprocess78.0ms (8.5%)

Memory

-27.4MiB live, 19.6MiB allocated; 2ms 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
▶	56.7%	(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

7.3MiB live, 7.3MiB 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)

rewrite37.0ms (4%)

Memory

-0.3MiB live, 46.1MiB allocated; 4ms 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: 6.8MiB live, 6.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 406 to 112 computations (72.4% saved)

prune2.0ms (0.2%)

Memory

3.6MiB live, 3.6MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	3	48

Accuracy

100.0%

Counts

48 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
▶	56.7%	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 13 to 10 computations (23.1% saved)

series3.0ms (0.4%)

Memory

5.6MiB live, 5.6MiB 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))))

rewrite67.0ms (7.2%)

Memory

18.6MiB live, 68.1MiB allocated; 4ms 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))))

eval3.0ms (0.3%)

Memory: 5.0MiB live, 5.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 204 to 71 computations (65.2% saved)

prune5.0ms (0.6%)

Memory

-39.9MiB live, 6.9MiB allocated; 3ms collecting garbage

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	31	2	33
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	31	5	36

Accuracy

100.0%

Counts

36 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	56.7%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	5.6%	(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)

rewrite38.0ms (4.1%)

Memory

-5.2MiB live, 41.8MiB allocated; 2ms 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))))

eval2.0ms (0.2%)

Memory: 3.9MiB live, 3.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 150 to 45 computations (70% saved)

prune3.0ms (0.3%)

Memory

7.5MiB live, 7.5MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	21	5	26

Accuracy

100.0%

Counts

26 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	56.7%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	5.6%	(sqrt.f64 #s(approx (* x (+ x x)) #s(literal 2 binary64)))

Compiler

Compiled 58 to 38 computations (34.5% saved)

regimes9.0ms (1%)

Memory

18.7MiB live, 18.7MiB 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	(*.f64 #s(literal 2 binary64) (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	(pow.f64 x #s(literal 2 binary64))

Results

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

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes10.0ms (1.1%)

Memory

-30.0MiB live, 15.4MiB allocated; 4ms 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:

5.0ms	(pow.f64 x #s(literal 2 binary64))
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)))

Results

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

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes4.0ms (0.4%)

Memory

11.5MiB live, 11.5MiB allocated; 0ms 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:

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
5.6%	1	`(pow.f64 x #s(literal 2 binary64))`
5.6%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
5.6%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
5.6%	1	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

derivations5.0ms (0.6%)

Memory

8.7MiB live, 8.7MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 15 to 9 computations (40% saved)

preprocess23.0ms (2.5%)

Memory: -14.1MiB live, 34.4MiB allocated; 9ms 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%)

sample563.0ms (61%)

explain60.0ms (6.5%)

preprocess78.0ms (8.5%)

series4.0ms (0.4%)

rewrite37.0ms (4%)

eval4.0ms (0.4%)

prune2.0ms (0.2%)

series3.0ms (0.4%)

rewrite67.0ms (7.2%)

eval3.0ms (0.3%)

prune5.0ms (0.6%)

series3.0ms (0.3%)

rewrite38.0ms (4.1%)

eval2.0ms (0.2%)

prune3.0ms (0.3%)

regimes9.0ms (1%)

regimes10.0ms (1.1%)

regimes4.0ms (0.4%)

derivations5.0ms (0.6%)

preprocess23.0ms (2.5%)

end0.0ms (0%)

Profiling