Metrics for sqrt A (should all be same)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB 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
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 10 to 4 computations (60% saved)

sample468.0ms (52.3%)

Memory

29.4MiB live, 939.7MiB allocated; 97ms collecting garbage

Samples

298.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 163.0ms

ival-hypot: 162.0ms (99.1% of total)

adjust: 2.0ms (1.2% of total)

Bogosity

explain62.0ms (6.9%)

Memory

6.4MiB live, 152.8MiB allocated; 6ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
104	-	4	(-2.3796313163679512e-158)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 x x))`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	uflow-rescue	55	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	underflow	55
↳	`(*.f64 x x)`	underflow	110
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	oflow-rescue	45	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	overflow	45
↳	`(*.f64 x x)`	overflow	90

Confusion

	Predicted +	Predicted -
+	100	4
-	0	152

Precision

1.0

Recall

0.9615384615384616

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	100	0	4
-	0	0	152

Precision?

1.0

Recall?

0.9615384615384616

Freqs

test

number	freq
0	156
1	100

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

26.0ms

512×

valid

Compiler

Compiled 50 to 16 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-hypot: 9.0ms (68.7% of total)

ival-mult!: 3.0ms (22.9% of total)

ival-add!: 1.0ms (7.6% of total)

adjust: 0.0ms (0% of total)

preprocess54.0ms (6%)

Memory

-29.2MiB live, 58.4MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	29	19
2	84	19
3	144	19
4	298	19
5	663	19
6	1542	19
7	3518	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.7%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Symmetry

(abs x)

Compiler

Compiled 16 to 8 computations (50% saved)

series4.0ms (0.4%)

Memory

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

Counts

4 → 5

Calls

Call 1

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

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

Calls

3 calls:

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

rewrite110.0ms (12.3%)

Memory

8.6MiB live, 195.3MiB allocated; 49ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	70
0	23	59
1	60	35
0	352	35

Stop Event

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

Counts

9 → 35

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(.f64 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(literal 2 binary64)
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.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 (fabs.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 (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 (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (+ (* x x) (* x x)) #s(literal 2 binary64))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

eval5.0ms (0.6%)

Memory: 15.7MiB live, 15.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 546 to 150 computations (72.5% saved)

prune4.0ms (0.5%)

Memory

10.8MiB live, 10.8MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	53	5	58
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	6	59

Accuracy

99.8%

Counts

59 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	17.2%	(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
▶	99.4%	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
▶	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
✓	62.7%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
▶	5.5%	(sqrt.f64 #s(approx (+ (* x x) (* x x)) #s(literal 2 binary64)))
▶	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 104 to 78 computations (25% saved)

series13.0ms (1.5%)

Memory

-23.2MiB live, 23.8MiB allocated; 1ms collecting garbage

Counts

23 → 23

Calls

Call 1

Inputs
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(sqrt.f64 x)
x
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
(sqrt.f64 #s(approx (+ (* x x) (* x x)) #s(literal 2 binary64)))
#s(approx (+ (* x x) (* x x)) #s(literal 2 binary64))
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(fabs.f64 x)
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(pow.f64 x #s(literal 6 binary64))
#s(literal 6 binary64)
(sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))
#s(literal 0 binary64)
(pow.f64 x #s(literal 4 binary64))
#s(literal 4 binary64)

Outputs
#s(approx (* (sqrt x) (sqrt (* 2 x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (* 2 x)) #s(hole binary64 (* (sqrt x) (sqrt 2))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (+ (* x x) (* x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* (sqrt 2) x) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (sqrt 2) (fabs x)) #s(hole binary64 (* (fabs x) (sqrt 2))))
#s(approx (fabs x) #s(hole binary64 (fabs x)))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (sqrt (* 2 (pow x 6))) #s(hole binary64 (* (pow x 3) (sqrt 2))))
#s(approx (* 2 (pow x 6)) #s(hole binary64 (* 2 (pow x 6))))
#s(approx (pow x 6) #s(hole binary64 (pow x 6)))
#s(approx (sqrt (+ 0 (pow x 4))) #s(hole binary64 (pow x 2)))
#s(approx (+ 0 (pow x 4)) #s(hole binary64 (pow x 4)))
#s(approx (pow x 4) #s(hole binary64 (pow x 4)))
#s(approx (* (sqrt x) (sqrt (* 2 x))) #s(hole binary64 (* -1 (* x (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (* 2 x)) #s(hole binary64 (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (sqrt (* 2 (pow x 6))) #s(hole binary64 (* -1 (* (pow x 3) (sqrt 2)))))

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	((* (sqrt x) (sqrt (* 2 x))) (sqrt x) x (sqrt (* 2 x)) (* 2 x) 2 (sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (* (sqrt 2) (fabs x)) (fabs x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)
4.0ms	x	@	inf	((* (sqrt x) (sqrt (* 2 x))) (sqrt x) x (sqrt (* 2 x)) (* 2 x) 2 (sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (* (sqrt 2) (fabs x)) (fabs x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)
4.0ms	x	@	0	((* (sqrt x) (sqrt (* 2 x))) (sqrt x) x (sqrt (* 2 x)) (* 2 x) 2 (sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (* (sqrt 2) (fabs x)) (fabs x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)

Time

Variable

Point

Expression

5.0ms

-inf

((* (sqrt x) (sqrt (* 2 x))) (sqrt x) x (sqrt (* 2 x)) (* 2 x) 2 (sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (* (sqrt 2) (fabs x)) (fabs x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)

4.0ms

inf

((* (sqrt x) (sqrt (* 2 x))) (sqrt x) x (sqrt (* 2 x)) (* 2 x) 2 (sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (* (sqrt 2) (fabs x)) (fabs x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)

4.0ms

((* (sqrt x) (sqrt (* 2 x))) (sqrt x) x (sqrt (* 2 x)) (* 2 x) 2 (sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (* (sqrt 2) (fabs x)) (fabs x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)

rewrite46.0ms (5.1%)

Memory

-2.7MiB live, 47.5MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	364
0	109	315
0	241	297

Stop Event

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

Counts

46 → 106

Calls

Call 1

Inputs
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(sqrt.f64 x)
x
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
(sqrt.f64 #s(approx (+ (* x x) (* x x)) #s(literal 2 binary64)))
#s(approx (+ (* x x) (* x x)) #s(literal 2 binary64))
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(fabs.f64 x)
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(pow.f64 x #s(literal 6 binary64))
#s(literal 6 binary64)
(sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))
#s(literal 0 binary64)
(pow.f64 x #s(literal 4 binary64))
#s(literal 4 binary64)
#s(approx (* (sqrt x) (sqrt (* 2 x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (* 2 x)) #s(hole binary64 (* (sqrt x) (sqrt 2))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (+ (* x x) (* x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* (sqrt 2) x) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (sqrt 2) (fabs x)) #s(hole binary64 (* (fabs x) (sqrt 2))))
#s(approx (fabs x) #s(hole binary64 (fabs x)))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (sqrt (* 2 (pow x 6))) #s(hole binary64 (* (pow x 3) (sqrt 2))))
#s(approx (* 2 (pow x 6)) #s(hole binary64 (* 2 (pow x 6))))
#s(approx (pow x 6) #s(hole binary64 (pow x 6)))
#s(approx (sqrt (+ 0 (pow x 4))) #s(hole binary64 (pow x 2)))
#s(approx (+ 0 (pow x 4)) #s(hole binary64 (pow x 4)))
#s(approx (pow x 4) #s(hole binary64 (pow x 4)))
#s(approx (* (sqrt x) (sqrt (* 2 x))) #s(hole binary64 (* -1 (* x (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (* 2 x)) #s(hole binary64 (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (sqrt (* 2 (pow x 6))) #s(hole binary64 (* -1 (* (pow x 3) (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)))
(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)
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 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 x x)
#s(literal 2 binary64)
(pow.f64 #s(approx (+ (* x x) (* x x)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (+ (* x x) (* x x)) #s(literal 2 binary64)))
#s(approx (+ (* x x) (* x x)) #s(literal 2 binary64))
#s(approx (* (sqrt x) (sqrt (* 2 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))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(sqrt.f64 (*.f64 x x))
(fabs.f64 (neg.f64 x))
(fabs.f64 x)
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))) (sqrt.f64 (pow.f64 x #s(literal 4 binary64))))
(sqrt.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 x #s(literal 6 binary64))))
(pow.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64)))
(hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))
(+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))
(pow.f64 x #s(literal 6 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 6 binary64)))
#s(literal 6 binary64)
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(.f64 (.f64 x x) (*.f64 x x))
(pow.f64 x #s(literal 4 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))
(+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))
#s(literal 0 binary64)
(.f64 (.f64 x x) (*.f64 x x))
(pow.f64 x #s(literal 4 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))
(+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))
#s(literal 4 binary64)
#s(approx (* (sqrt x) (sqrt (* 2 x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx x x)
#s(approx (sqrt (* 2 x)) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
#s(approx (* 2 x) (*.f64 #s(literal 2 binary64) x))
#s(approx (* (sqrt x) (sqrt (* 2 x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (+ (* x x) (* x x)) (.f64 (.f64 x x) #s(literal 2 binary64)))
#s(approx (* (sqrt 2) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (* (sqrt 2) (fabs x)) (*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (fabs x) (fabs.f64 x))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (* 2 (pow x 6))) (*.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* 2 (pow x 6)) (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64)))
#s(approx (pow x 6) (pow.f64 x #s(literal 6 binary64)))
#s(approx (sqrt (+ 0 (pow x 4))) (*.f64 x x))
#s(approx (+ 0 (pow x 4)) (pow.f64 x #s(literal 4 binary64)))
#s(approx (+ 0 (pow x 4)) (pow.f64 x #s(literal 4 binary64)))
#s(approx (* (sqrt x) (sqrt (* 2 x))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
#s(approx (sqrt x) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 x))))
#s(approx (sqrt (* 2 x)) (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x))))
#s(approx (* (sqrt x) (sqrt (* 2 x))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
#s(approx (sqrt (* 2 (pow x 6))) (neg.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))

eval7.0ms (0.8%)

Memory: 13.5MiB live, 13.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 221 to 241 computations (80.3% saved)

prune5.0ms (0.6%)

Memory

15.2MiB live, 15.2MiB allocated; 0ms collecting garbage

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	0	0	0
Picked	2	3	5
Done	1	0	1
Total	111	7	118

Accuracy

100.0%

Counts

118 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	18.5%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(approx (sqrt (+ 0 (pow x 4))) (.f64 x x)))
▶	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
▶	62.7%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	5.5%	(sqrt.f64 #s(approx (+ (* x x) (* x x)) #s(literal 2 binary64)))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 61 to 45 computations (26.2% saved)

series9.0ms (1%)

Memory

-29.9MiB live, 18.2MiB allocated; 3ms collecting garbage

Counts

16 → 21

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 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 x)
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(approx (sqrt (+ 0 (pow x 4))) (.f64 x x)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(pow.f64 x #s(literal 6 binary64))
#s(literal 6 binary64)
#s(approx (sqrt (+ 0 (pow x 4))) (*.f64 x 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 x) (sqrt (+ x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* (sqrt x) (sqrt 2))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (sqrt (* 2 (pow x 6))) #s(hole binary64 (* (pow x 3) (sqrt 2))))
#s(approx (* 2 (pow x 6)) #s(hole binary64 (* 2 (pow x 6))))
#s(approx (pow x 6) #s(hole binary64 (pow x 6)))
#s(approx (sqrt (+ 0 (pow x 4))) #s(hole binary64 (pow x 2)))
#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) (sqrt (+ x x))) #s(hole binary64 (* -1 (* x (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (sqrt (* 2 (pow x 6))) #s(hole binary64 (* -1 (* (pow x 3) (sqrt 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	@	0	((sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) x 2 (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (+ x x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (sqrt (+ (* x x) (* x x))))
3.0ms	x	@	-inf	((sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) x 2 (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (+ x x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (sqrt (+ (* x x) (* x x))))
2.0ms	x	@	inf	((sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) x 2 (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (+ x x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (sqrt (+ (* x x) (* x x))))

Time

Variable

Point

Expression

3.0ms

((sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) x 2 (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (+ x x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (sqrt (+ (* x x) (* x x))))

3.0ms

-inf

((sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) x 2 (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (+ x x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (sqrt (+ (* x x) (* x x))))

2.0ms

inf

((sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) x 2 (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (+ x x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (sqrt (+ (* x x) (* x x))))

rewrite31.0ms (3.4%)

Memory

-5.7MiB live, 41.3MiB allocated; 1ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	312
0	94	261
0	231	261

Stop Event

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

Counts

37 → 130

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 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 x)
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(approx (sqrt (+ 0 (pow x 4))) (.f64 x x)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(pow.f64 x #s(literal 6 binary64))
#s(literal 6 binary64)
#s(approx (sqrt (+ 0 (pow x 4))) (*.f64 x 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 x) (sqrt (+ x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* (sqrt x) (sqrt 2))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (sqrt (* 2 (pow x 6))) #s(hole binary64 (* (pow x 3) (sqrt 2))))
#s(approx (* 2 (pow x 6)) #s(hole binary64 (* 2 (pow x 6))))
#s(approx (pow x 6) #s(hole binary64 (pow x 6)))
#s(approx (sqrt (+ 0 (pow x 4))) #s(hole binary64 (pow x 2)))
#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) (sqrt (+ x x))) #s(hole binary64 (* -1 (* x (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (sqrt (* 2 (pow x 6))) #s(hole binary64 (* -1 (* (pow x 3) (sqrt 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)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(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 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.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))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(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 (sqrt.f64 (.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(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)
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 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)
(/.f64 (neg.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64)))) (neg.f64 #s(approx (sqrt (+ 0 (pow x 4))) (.f64 x x))))
(/.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))) #s(approx (sqrt (+ 0 (pow x 4))) (.f64 x x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 x #s(literal 6 binary64))))
(pow.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64)))
(hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))
(+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))
(pow.f64 x #s(literal 6 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 6 binary64)))
#s(literal 6 binary64)
#s(approx (sqrt (+ 0 (pow x 4))) (*.f64 x x))
(.f64 (sqrt.f64 (.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(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 (* (* x x) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt x) (sqrt.f64 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 (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (* 2 (pow x 6))) (*.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* 2 (pow x 6)) (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64)))
#s(approx (pow x 6) (pow.f64 x #s(literal 6 binary64)))
#s(approx (sqrt (+ 0 (pow x 4))) (*.f64 x 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) 2)) (neg.f64 (*.f64 (sqrt.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)) (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x))))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
#s(approx (sqrt (* 2 (pow x 6))) (neg.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (* (* x x) 2)) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

eval8.0ms (0.9%)

Memory: 18.1MiB live, 18.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 249 to 238 computations (80.9% saved)

prune6.0ms (0.7%)

Memory

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

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	0	0
Picked	0	4	4
Done	0	3	3
Total	109	7	116

Accuracy

100.0%

Counts

116 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	18.5%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(approx (sqrt (+ 0 (pow x 4))) (.f64 x x)))
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
✓	62.7%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	5.5%	(sqrt.f64 #s(approx (+ (* x x) (* x x)) #s(literal 2 binary64)))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 150 to 87 computations (42% saved)

regimes13.0ms (1.4%)

Memory

-21.9MiB live, 25.1MiB allocated; 2ms collecting garbage

Counts

10 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (+ (* x x) (* x x)) #s(literal 2 binary64)))
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(hypot.f64 x x)
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(approx (sqrt (+ 0 (pow x 4))) (.f64 x x)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))

Outputs
(hypot.f64 x x)

Calls

4 calls:

3.0ms	x
3.0ms	(+.f64 (.f64 x x) (.f64 x x))
3.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	1	`(*.f64 x x)`
100.0%	1	`(+.f64 (.f64 x x) (.f64 x x))`
100.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
100.0%	1	`x`

Compiler

Compiled 19 to 10 computations (47.4% saved)

regimes9.0ms (1%)

Memory

19.7MiB live, 19.7MiB allocated; 0ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	(*.f64 x x)
2.0ms	(+.f64 (.f64 x x) (.f64 x x))

Results

Accuracy	Segments	Branch
99.4%	1	`(*.f64 x x)`
99.4%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.4%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.4%	1	`x`

Compiler

Compiled 19 to 10 computations (47.4% saved)

regimes11.0ms (1.2%)

Memory

-29.8MiB live, 20.1MiB allocated; 4ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

5.0ms	(*.f64 x x)
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	(+.f64 (.f64 x x) (.f64 x x))

Results

Accuracy	Segments	Branch
99.3%	1	`(*.f64 x x)`
99.3%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.3%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.3%	1	`x`

Compiler

Compiled 19 to 10 computations (47.4% saved)

regimes4.0ms (0.4%)

Memory

11.0MiB live, 11.0MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

1.0ms	x
1.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
1.0ms	(+.f64 (.f64 x x) (.f64 x x))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
5.5%	1	`(*.f64 x x)`
5.5%	1	`(+.f64 (.f64 x x) (.f64 x x))`
5.5%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
5.5%	1	`x`

Compiler

Compiled 19 to 10 computations (47.4% saved)

derivations7.0ms (0.8%)

Memory

13.2MiB live, 13.2MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 33 to 15 computations (54.5% saved)

preprocess19.0ms (2.1%)

Memory: -8.3MiB live, 38.1MiB allocated; 2ms collecting garbage
Remove: (abs x)
Compiler: Compiled 148 to 80 computations (45.9% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample468.0ms (52.3%)

explain62.0ms (6.9%)

preprocess54.0ms (6%)

series4.0ms (0.4%)

rewrite110.0ms (12.3%)

eval5.0ms (0.6%)

prune4.0ms (0.5%)

series13.0ms (1.5%)

rewrite46.0ms (5.1%)

eval7.0ms (0.8%)

prune5.0ms (0.6%)

series9.0ms (1%)

rewrite31.0ms (3.4%)

eval8.0ms (0.9%)

prune6.0ms (0.7%)

regimes13.0ms (1.4%)

regimes9.0ms (1%)

regimes11.0ms (1.2%)

regimes4.0ms (0.4%)

derivations7.0ms (0.8%)

preprocess19.0ms (2.1%)

end0.0ms (0%)

Profiling