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

0.5MiB live, 0.5MiB 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)

sample500.0ms (39.7%)

Memory

25.5MiB live, 690.5MiB allocated; 88ms collecting garbage

Samples

320.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 143.0ms

ival-mult!: 80.0ms (55.8% of total)

ival-sqrt: 61.0ms (42.5% of total)

adjust: 2.0ms (1.4% of total)

Bogosity

explain55.0ms (4.4%)

Memory

-3.5MiB live, 92.4MiB allocated; 9ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
124	-	-	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(*.f64 x x)`
0	-	-	`(.f64 #s(literal 2 binary64) (.f64 x x))`
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	64	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	overflow	64
↳	`(*.f64 x x)`	overflow	64
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	uflow-rescue	60	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	underflow	60
↳	`(*.f64 x x)`	underflow	60

Confusion

	Predicted +	Predicted -
+	124	0
-	0	132

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	124	0	0
-	0	0	132

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	132
1	124

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

25.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

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

ival-sqrt: 7.0ms (59.3% of total)

ival-mult!: 5.0ms (42.4% of total)

adjust: 0.0ms (0% of total)

preprocess304.0ms (24.1%)

Memory

18.6MiB live, 245.6MiB allocated; 55ms 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

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

series4.0ms (0.3%)

Memory

5.8MiB live, 5.8MiB 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
1.0ms	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)

rewrite36.0ms (2.8%)

Memory

-10.6MiB live, 36.6MiB 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: 11.2MiB live, 11.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 563 to 158 computations (71.9% saved)

prune3.0ms (0.2%)

Memory

4.1MiB live, 4.1MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	63	4	67
Fresh	0	0	0
Picked	1	0	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)
▶	99.5%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
▶	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
▶	54.9%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))

Compiler

Compiled 20 to 17 computations (15% saved)

series7.0ms (0.5%)

Memory

8.0MiB live, 8.0MiB allocated; 0ms collecting garbage

Counts

12 → 15

Calls

Call 1

Inputs
(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 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(.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 (* (* 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 x #s(hole binary64 x))
#s(approx (* (sqrt 2) x) #s(hole binary64 (* x (sqrt 2))))
#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 x) 2)) #s(hole binary64 (* -1 (* 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
4.0ms	x	@	-inf	((sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) x 2 (* (sqrt 2) x) (sqrt 2) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (sqrt (+ (* x x) (* x x))))
1.0ms	x	@	inf	((sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) x 2 (* (sqrt 2) x) (sqrt 2) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (sqrt (+ (* x x) (* x x))))
1.0ms	x	@	0	((sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) x 2 (* (sqrt 2) x) (sqrt 2) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (sqrt (+ (* x x) (* x x))))

Time

Variable

Point

Expression

4.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

rewrite57.0ms (4.5%)

Memory

-24.4MiB live, 26.3MiB allocated; 27ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	191
0	66	163
0	146	163

Stop Event

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

Counts

27 → 92

Calls

Call 1

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

eval7.0ms (0.6%)

Memory: 8.7MiB live, 8.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 653 to 163 computations (75% saved)

prune4.0ms (0.3%)

Memory

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

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	0	0	0
Picked	4	0	4
Done	0	0	0
Total	85	4	89

Accuracy

100.0%

Counts

89 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 #s(approx x x) x)
▶	99.5%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
▶	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx x x))
▶	54.9%	(sqrt.f64 (.f64 (.f64 #s(approx x x) x) #s(literal 2 binary64)))

Compiler

Compiled 26 to 19 computations (26.9% saved)

series5.0ms (0.4%)

Memory

5.1MiB live, 5.1MiB allocated; 0ms collecting garbage

Counts

13 → 15

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

2.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

rewrite56.0ms (4.5%)

Memory

-33.1MiB live, 15.1MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	214
0	70	191
0	184	179

Stop Event

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

Counts

28 → 73

Calls

Call 1

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

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

eval7.0ms (0.5%)

Memory: 7.7MiB live, 7.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 647 to 138 computations (78.7% saved)

prune4.0ms (0.3%)

Memory

4.5MiB live, 4.5MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	0	0
Picked	4	0	4
Done	0	0	0
Total	80	4	84

Accuracy

100.0%

Counts

84 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 #s(approx x x) x)
▶	99.5%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
▶	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx x x))
▶	54.9%	(sqrt.f64 (.f64 (.f64 #s(approx x x) x) #s(literal 2 binary64)))

Compiler

Compiled 26 to 19 computations (26.9% saved)

series5.0ms (0.4%)

Memory

4.8MiB live, 4.8MiB allocated; 0ms collecting garbage

Counts

13 → 15

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

2.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

rewrite25.0ms (2%)

Memory

11.1MiB live, 11.1MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	214
0	70	191
0	184	179

Stop Event

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

Counts

28 → 73

Calls

Call 1

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

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

eval7.0ms (0.5%)

Memory: 11.2MiB live, 11.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 647 to 138 computations (78.7% saved)

prune10.0ms (0.8%)

Memory

-33.0MiB live, 12.6MiB allocated; 3ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	0	0
Picked	4	0	4
Done	0	0	0
Total	80	4	84

Accuracy

100.0%

Counts

84 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
	100.0%	(hypot.f64 #s(approx x x) x)
	99.5%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx x x))
	54.9%	(sqrt.f64 (.f64 (.f64 #s(approx x x) x) #s(literal 2 binary64)))

Compiler

Compiled 130 to 42 computations (67.7% saved)

regimes17.0ms (1.4%)

Memory

24.9MiB live, 24.9MiB allocated; 0ms collecting garbage

Counts

17 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

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

regimes16.0ms (1.3%)

Memory

-20.7MiB live, 24.1MiB allocated; 4ms collecting garbage

Counts

13 → 1

Calls

Call 1

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

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

Calls

4 calls:

6.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))
4.0ms	x
3.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.5%	1	`(*.f64 x x)`
99.5%	1	`(.f64 #s(literal 2 binary64) (.f64 x x))`
99.5%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
99.5%	1	`x`

Compiler

Compiled 15 to 12 computations (20% saved)

regimes10.0ms (0.8%)

Memory

17.2MiB live, 17.2MiB allocated; 0ms collecting garbage

Accuracy

Total -28.6b remaining (-7184.4%)

Threshold costs -28.6b (-7184.4%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	x
2.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))
2.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
2.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 15 to 12 computations (20% saved)

derivations6.0ms (0.5%)

Memory

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

Stop Event

1×

fuel

Compiler

Compiled 14 to 9 computations (35.7% saved)

preprocess110.0ms (8.7%)

Memory: -38.4MiB live, 25.1MiB allocated; 135ms collecting garbage
Compiler: Compiled 68 to 50 computations (26.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample500.0ms (39.7%)

explain55.0ms (4.4%)

preprocess304.0ms (24.1%)

eval0.0ms (0%)

prune0.0ms (0%)

series4.0ms (0.3%)

rewrite36.0ms (2.8%)

eval7.0ms (0.5%)

prune3.0ms (0.2%)

series7.0ms (0.5%)

rewrite57.0ms (4.5%)

eval7.0ms (0.6%)

prune4.0ms (0.3%)

series5.0ms (0.4%)

rewrite56.0ms (4.5%)

eval7.0ms (0.5%)

prune4.0ms (0.3%)

series5.0ms (0.4%)

rewrite25.0ms (2%)

eval7.0ms (0.5%)

prune10.0ms (0.8%)

regimes17.0ms (1.4%)

regimes16.0ms (1.3%)

regimes10.0ms (0.8%)

derivations6.0ms (0.5%)

preprocess110.0ms (8.7%)

end0.0ms (0%)

Profiling