Metrics for sqrt C (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
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample479.0ms (39.3%)

Memory

8.8MiB live, 463.9MiB allocated; 61ms collecting garbage

Samples

302.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 157.0ms

ival-mult!: 83.0ms (52.9% of total)

ival-sqrt: 73.0ms (46.5% of total)

adjust: 1.0ms (0.6% of total)

Bogosity

explain60.0ms (5%)

Memory

-12.8MiB live, 80.2MiB allocated; 21ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
133	-	3	(-1.4014202631436172e-158)	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`(.f64 #s(literal 2 binary64) (.f64 x x))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	oflow-rescue	77	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	overflow	77
↳	`(*.f64 x x)`	overflow	77
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	uflow-rescue	53	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	underflow	53
↳	`(*.f64 x x)`	underflow	53

Confusion

	Predicted +	Predicted -
+	130	3
-	0	123

Precision

1.0

Recall

0.9774436090225563

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	130	0	3
-	0	0	123

Precision?

1.0

Recall?

0.9774436090225563

Freqs

test

number	freq
0	126
1	130

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

19.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

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

ival-mult!: 5.0ms (56.6% of total)

ival-sqrt: 4.0ms (45.3% of total)

adjust: 0.0ms (0% of total)

preprocess422.0ms (34.6%)

Memory

15.7MiB live, 223.8MiB allocated; 73ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	28	19
2	90	19
3	185	19
4	578	19
5	1314	19
6	4975	19
0	5	6
0	8	6
1	18	6
2	61	6
3	182	6
4	501	6
5	1234	6
6	4730	6
7	7915	6
0	8495	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) (.f64 x x)))

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

Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.0MiB 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
▶	52.2%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

series4.0ms (0.3%)

Memory

4.0MiB live, 4.0MiB allocated; 0ms collecting garbage

Counts

5 → 5

Calls

Call 1

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

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

Calls

3 calls:

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

rewrite66.0ms (5.4%)

Memory

-17.9MiB live, 28.5MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	61
0	22	60
1	50	54
0	171	49

Stop Event

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

Counts

10 → 65

Calls

Call 1

Inputs
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(.f64 #s(literal 2 binary64) (.f64 x x))
#s(literal 2 binary64)
(*.f64 x x)
x
#s(approx (sqrt (* 2 (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* 2 (* x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (* 2 (* x x))) #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 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 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 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 x))
(hypot.f64 (neg.f64 (neg.f64 x)) x)
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 x))
(hypot.f64 (exp.f64 (log.f64 x)) x)
(hypot.f64 (neg.f64 x) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 x) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (neg.f64 (neg.f64 x)))
(hypot.f64 x (exp.f64 (log.f64 x)))
(hypot.f64 x (neg.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) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 x #s(literal 2 binary64)) x)
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 2 binary64)))
(*.f64 (neg.f64 x) (fma.f64 #s(literal -1 binary64) x (neg.f64 x)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 x (.f64 x #s(literal 2 binary64)))
(.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 (neg.f64 x)) (neg.f64 (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 (neg.f64 x) (neg.f64 x) (*.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 x (neg.f64 x)))
(-.f64 (.f64 x x) (.f64 (neg.f64 (neg.f64 x)) (neg.f64 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 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 x (neg.f64 x)))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
x
#s(approx (sqrt (* 2 (* x x))) (hypot.f64 x x))
#s(approx (* 2 (* x x)) (.f64 (.f64 x x) #s(literal 2 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (sqrt (* 2 (* x x))) (neg.f64 (hypot.f64 x x)))

eval7.0ms (0.5%)

Memory: 6.1MiB live, 6.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 563 to 158 computations (71.9% saved)

prune3.0ms (0.3%)

Memory

5.8MiB live, 5.8MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	4	68

Accuracy

100.0%

Counts

68 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	99.2%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
▶	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	52.2%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 20 to 17 computations (15% saved)

series5.0ms (0.4%)

Memory

6.9MiB live, 6.9MiB allocated; 0ms collecting garbage

Counts

9 → 11

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

3.0ms

-inf

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

1.0ms

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

1.0ms

inf

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

rewrite33.0ms (2.7%)

Memory

-23.4MiB live, 21.5MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	135
0	52	117
0	123	117

Stop Event

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

Counts

20 → 44

Calls

Call 1

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

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

eval4.0ms (0.4%)

Memory: 9.1MiB live, 9.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 377 to 95 computations (74.8% saved)

prune3.0ms (0.3%)

Memory

7.2MiB live, 7.2MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	52	5	57

Accuracy

100.0%

Counts

57 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	99.1%	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
▶	99.2%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	52.2%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 28 to 22 computations (21.4% saved)

series4.0ms (0.4%)

Memory

7.6MiB live, 7.6MiB allocated; 0ms collecting garbage

Counts

9 → 12

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

3.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

rewrite44.0ms (3.6%)

Memory

-37.1MiB live, 16.3MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	176
0	56	139
0	136	139

Stop Event

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

Counts

21 → 41

Calls

Call 1

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

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

eval4.0ms (0.3%)

Memory: 4.2MiB live, 4.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 466 to 107 computations (77% saved)

prune3.0ms (0.3%)

Memory

4.0MiB live, 4.0MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	47	5	52

Accuracy

100.0%

Counts

52 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.1%	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
✓	99.2%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	52.2%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 63 to 39 computations (38.1% saved)

regimes9.0ms (0.7%)

Memory

8.9MiB live, 8.9MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

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

Results

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

Compiler

Compiled 15 to 12 computations (20% saved)

regimes8.0ms (0.6%)

Memory

13.7MiB live, 13.7MiB allocated; 0ms collecting garbage

Accuracy

Total -30.5b remaining (-7091.8%)

Threshold costs -30.5b (-7091.8%)

Counts

5 → 1

Calls

Call 1

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

Results

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

Compiler

Compiled 15 to 12 computations (20% saved)

simplify35.0ms (2.9%)

Memory

-6.0MiB live, 40.8MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	7	7
2	10	7
3	16	7
4	48	7
5	370	7
6	3460	7

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations2.0ms (0.2%)

Memory

1.8MiB live, 1.8MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 7 to 5 computations (28.6% saved)

preprocess21.0ms (1.8%)

Memory: -23.1MiB live, 20.8MiB allocated; 5ms collecting garbage
Remove: (abs x)
Compiler: Compiled 32 to 24 computations (25% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample479.0ms (39.3%)

explain60.0ms (5%)

preprocess422.0ms (34.6%)

eval0.0ms (0%)

prune0.0ms (0%)

series4.0ms (0.3%)

rewrite66.0ms (5.4%)

eval7.0ms (0.5%)

prune3.0ms (0.3%)

series5.0ms (0.4%)

rewrite33.0ms (2.7%)

eval4.0ms (0.4%)

prune3.0ms (0.3%)

series4.0ms (0.4%)

rewrite44.0ms (3.6%)

eval4.0ms (0.3%)

prune3.0ms (0.3%)

regimes9.0ms (0.7%)

regimes8.0ms (0.6%)

simplify35.0ms (2.9%)

derivations2.0ms (0.2%)

preprocess21.0ms (1.8%)

end0.0ms (0%)

Profiling