Metrics for sqrt B (should all be same)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

1.0MiB live, 1.0MiB 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)

sample554.0ms (63.1%)

Memory

-1.0MiB live, 847.6MiB allocated; 141ms collecting garbage

Samples

345.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 142.0ms

ival-mult!: 78.0ms (54.9% of total)

ival-sqrt: 63.0ms (44.4% of total)

adjust: 2.0ms (1.4% of total)

Bogosity

explain51.0ms (5.8%)

Memory

25.4MiB live, 73.2MiB allocated; 2ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
123	-	2	(-1.8457506386685487e-156)	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(.f64 (.f64 #s(literal 2 binary64) x) x)`
0	-	0	-	`(*.f64 #s(literal 2 binary64) x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`	oflow-rescue	67	0
↳	`(.f64 (.f64 #s(literal 2 binary64) x) x)`	overflow	67
`sqrt.f64`	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`	uflow-rescue	54	0
↳	`(.f64 (.f64 #s(literal 2 binary64) x) x)`	underflow	54

Confusion

	Predicted +	Predicted -
+	121	2
-	0	133

Precision

1.0

Recall

0.983739837398374

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	121	0	2
-	0	0	133

Precision?

1.0

Recall?

0.983739837398374

Freqs

test

number	freq
0	135
1	121

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

21.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult!: 6.0ms (57% of total)

ival-sqrt: 4.0ms (38% of total)

adjust: 0.0ms (0% of total)

preprocess76.0ms (8.6%)

Memory

-27.8MiB live, 19.3MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	25	19
2	62	19
3	196	19
4	333	19
5	1011	19
6	4908	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.6%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Symmetry

(abs x)

Compiler

Compiled 12 to 10 computations (16.7% saved)

series4.0ms (0.5%)

Memory

5.7MiB live, 5.7MiB allocated; 0ms collecting garbage

Counts

5 → 5

Calls

Call 1

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

rewrite69.0ms (7.8%)

Memory

-6.7MiB live, 50.1MiB allocated; 38ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	61
0	22	60
1	48	60
0	150	51

Stop Event

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

Counts

10 → 58

Calls

Call 1

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

eval5.0ms (0.6%)

Memory: 8.8MiB live, 8.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 513 to 135 computations (73.7% saved)

prune3.0ms (0.4%)

Memory

6.0MiB live, 6.0MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	55	5	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	5	61

Accuracy

100.0%

Counts

61 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	99.4%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
▶	55.6%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	99.4%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	2.0%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 78 to 62 computations (20.5% saved)

series7.0ms (0.8%)

Memory

10.1MiB live, 10.1MiB allocated; 0ms collecting garbage

Counts

16 → 19

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

3.0ms

-inf

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

2.0ms

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

2.0ms

inf

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

rewrite29.0ms (3.3%)

Memory

-25.4MiB live, 24.2MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	263
0	85	211
0	175	211

Stop Event

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

Counts

35 → 127

Calls

Call 1

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

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

eval7.0ms (0.8%)

Memory: 12.4MiB live, 12.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 909 to 194 computations (78.7% saved)

prune6.0ms (0.6%)

Memory

9.4MiB live, 9.4MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	0	0
Picked	0	5	5
Done	0	0	0
Total	94	6	100

Accuracy

100.0%

Counts

100 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	99.0%	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
✓	99.4%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
✓	55.6%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.4%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	2.0%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 47 to 37 computations (21.3% saved)

series3.0ms (0.4%)

Memory

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

Counts

6 → 7

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

2.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

rewrite21.0ms (2.4%)

Memory

-31.0MiB live, 16.2MiB allocated; 1ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	101
0	32	82
0	77	82

Stop Event

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

Counts

13 → 18

Calls

Call 1

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

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

eval1.0ms (0.2%)

Memory: 2.5MiB live, 2.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 241 to 53 computations (78% saved)

prune3.0ms (0.3%)

Memory

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

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	24	6	30

Accuracy

100.0%

Counts

30 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.0%	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
✓	99.4%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
✓	55.6%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.4%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	2.0%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 100 to 62 computations (38% saved)

regimes7.0ms (0.8%)

Memory

11.7MiB live, 11.7MiB allocated; 0ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

3 calls:

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

Results

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

Compiler

Compiled 12 to 10 computations (16.7% saved)

regimes6.0ms (0.7%)

Memory

10.1MiB live, 10.1MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 12 to 10 computations (16.7% saved)

regimes5.0ms (0.6%)

Memory

8.6MiB live, 8.6MiB allocated; 0ms collecting garbage

Accuracy

Total -62.3b remaining (-15188.5%)

Threshold costs -62.3b (-15188.5%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	x
2.0ms	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
1.0ms	(.f64 (.f64 #s(literal 2 binary64) x) x)

Results

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

Compiler

Compiled 12 to 10 computations (16.7% saved)

derivations4.0ms (0.5%)

Memory

3.8MiB live, 3.8MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 21 to 14 computations (33.3% saved)

preprocess15.0ms (1.8%)

Memory: -24.5MiB live, 23.1MiB allocated; 2ms collecting garbage
Compiler: Compiled 96 to 72 computations (25% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample554.0ms (63.1%)

explain51.0ms (5.8%)

preprocess76.0ms (8.6%)

series4.0ms (0.5%)

rewrite69.0ms (7.8%)

eval5.0ms (0.6%)

prune3.0ms (0.4%)

series7.0ms (0.8%)

rewrite29.0ms (3.3%)

eval7.0ms (0.8%)

prune6.0ms (0.6%)

series3.0ms (0.4%)

rewrite21.0ms (2.4%)

eval1.0ms (0.2%)

prune3.0ms (0.3%)

regimes7.0ms (0.8%)

regimes6.0ms (0.7%)

regimes5.0ms (0.6%)

derivations4.0ms (0.5%)

preprocess15.0ms (1.8%)

end0.0ms (0%)

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