Metrics for sqrt A (should all be same)

start0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB 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
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 10 to 4 computations (60% saved)

sample506.0ms (36.6%)

Memory

9.9MiB live, 613.0MiB allocated; 113ms collecting garbage

Samples

361.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 204.0ms

ival-hypot: 203.0ms (99.4% of total)

adjust: 1.0ms (0.5% of total)

Bogosity

explain59.0ms (4.3%)

Memory

35.5MiB live, 82.6MiB allocated; 3ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
112	-	1	(7.983644412343856e-161)	`(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)))`	oflow-rescue	65	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	overflow	65
↳	`(*.f64 x x)`	overflow	130
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	uflow-rescue	46	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	underflow	46
↳	`(*.f64 x x)`	underflow	92

Confusion

	Predicted +	Predicted -
+	111	1
-	0	144

Precision

1.0

Recall

0.9910714285714286

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	111	0	1
-	0	0	144

Precision?

1.0

Recall?

0.9910714285714286

Freqs

test

number	freq
0	145
1	111

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

23.0ms

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 (70.5% of total)

ival-mult!: 3.0ms (23.5% of total)

ival-add!: 1.0ms (7.8% of total)

adjust: 0.0ms (0% of total)

preprocess50.0ms (3.7%)

Memory

3.6MiB live, 50.9MiB allocated; 1ms 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
▶	59.3%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Symmetry

(abs x)

Compiler

Compiled 16 to 8 computations (50% saved)

series9.0ms (0.7%)

Memory

-40.1MiB live, 9.9MiB allocated; 3ms 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
7.0ms	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)

rewrite411.0ms (29.7%)

Memory

-21.3MiB live, 115.8MiB allocated; 663ms 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 (0.3%)

Memory: 6.1MiB live, 6.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 498 to 148 computations (70.3% saved)

prune5.0ms (0.3%)

Memory

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

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	7	53

Accuracy

99.7%

Counts

53 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	23.7%	(/.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)))))
▶	99.3%	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
▶	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
▶	56.4%	(sqrt.f64 (+.f64 (pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64)) (*.f64 x x)))
✓	59.3%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
▶	5.9%	(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 124 to 94 computations (24.2% saved)

series142.0ms (10.3%)

Memory

6.3MiB live, 142.1MiB allocated; 123ms collecting garbage

Counts

19 → 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)
(sqrt.f64 (+.f64 (pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64)) (*.f64 x x)))
(+.f64 (pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64)) (*.f64 x x))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(exp.f64 (log.f64 x))
(log.f64 x)
(*.f64 x x)

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 (+ (pow (exp (log x)) 2) (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (+ (pow (exp (log x)) 2) (* x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (pow (exp (log x)) 2) #s(hole binary64 (pow x 2)))
#s(approx (exp (log x)) #s(hole binary64 x))
#s(approx (log x) #s(hole binary64 (log x)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (log x) #s(hole binary64 (* -1 (log (/ 1 x)))))
#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 (+ (pow (exp (log x)) 2) (* x x))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (log x) #s(hole binary64 (+ (log -1) (* -1 (log (/ -1 x))))))

Calls

3 calls:

Time	Variable		Point	Expression
89.0ms	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 (+ (pow (exp (log x)) 2) (* x x))) (+ (pow (exp (log x)) 2) (* x x)) (pow (exp (log x)) 2) (exp (log x)) (log x) (* x x))
44.0ms	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 (+ (pow (exp (log x)) 2) (* x x))) (+ (pow (exp (log x)) 2) (* x x)) (pow (exp (log x)) 2) (exp (log x)) (log x) (* x x))
9.0ms	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 (+ (pow (exp (log x)) 2) (* x x))) (+ (pow (exp (log x)) 2) (* x x)) (pow (exp (log x)) 2) (exp (log x)) (log x) (* x x))

Time

Variable

Point

Expression

89.0ms

((* (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 (+ (pow (exp (log x)) 2) (* x x))) (+ (pow (exp (log x)) 2) (* x x)) (pow (exp (log x)) 2) (exp (log x)) (log x) (* x x))

44.0ms

-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 (+ (pow (exp (log x)) 2) (* x x))) (+ (pow (exp (log x)) 2) (* x x)) (pow (exp (log x)) 2) (exp (log x)) (log x) (* x x))

9.0ms

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 (+ (pow (exp (log x)) 2) (* x x))) (+ (pow (exp (log x)) 2) (* x x)) (pow (exp (log x)) 2) (exp (log x)) (log x) (* x x))

rewrite55.0ms (4%)

Memory

-25.5MiB live, 58.3MiB allocated; 32ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	336
0	104	274
0	230	247

Stop Event

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

Counts

42 → 116

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

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

eval7.0ms (0.5%)

Memory: 22.7MiB live, 22.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 730 to 205 computations (71.9% saved)

prune3.0ms (0.2%)

Memory

5.9MiB live, 5.9MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	1	0	1
Picked	1	4	5
Done	1	0	1
Total	75	6	81

Accuracy

100.0%

Counts

81 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
✓	99.3%	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
▶	59.3%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	5.9%	(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 44 to 32 computations (27.3% saved)

series3.0ms (0.2%)

Memory

4.7MiB live, 4.7MiB allocated; 0ms collecting garbage

Counts

6 → 7

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

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

rewrite79.0ms (5.7%)

Memory

-20.3MiB live, 45.9MiB allocated; 42ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	82
0	28	67
1	69	45
0	335	45

Stop Event

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

Counts

13 → 44

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

eval3.0ms (0.2%)

Memory: 5.0MiB live, 5.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 215 to 94 computations (56.3% saved)

prune3.0ms (0.3%)

Memory

6.4MiB live, 6.4MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	29	6	35

Accuracy

100.0%

Counts

35 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.3%	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
✓	59.3%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	5.9%	(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 119 to 69 computations (42% saved)

regimes18.0ms (1.3%)

Memory

-26.9MiB live, 21.8MiB allocated; 10ms collecting garbage

Counts

9 → 1

Calls

Call 1

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

8.0ms	x
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
3.0ms	(*.f64 x x)
2.0ms	(+.f64 (.f64 x x) (.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)

regimes4.0ms (0.3%)

Memory

9.7MiB live, 9.7MiB 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
5.9%	1	`(*.f64 x x)`
5.9%	1	`(+.f64 (.f64 x x) (.f64 x x))`
5.9%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
5.9%	1	`x`

Compiler

Compiled 19 to 10 computations (47.4% saved)

derivations5.0ms (0.4%)

Memory

6.5MiB live, 6.5MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 13 to 7 computations (46.2% saved)

preprocess16.0ms (1.2%)

Memory: -17.5MiB live, 29.7MiB allocated; 2ms collecting garbage
Remove: (abs x)
Compiler: Compiled 68 to 38 computations (44.1% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample506.0ms (36.6%)

explain59.0ms (4.3%)

preprocess50.0ms (3.7%)

series9.0ms (0.7%)

rewrite411.0ms (29.7%)

eval5.0ms (0.3%)

prune5.0ms (0.3%)

series142.0ms (10.3%)

rewrite55.0ms (4%)

eval7.0ms (0.5%)

prune3.0ms (0.2%)

series3.0ms (0.2%)

rewrite79.0ms (5.7%)

eval3.0ms (0.2%)

prune3.0ms (0.3%)

regimes18.0ms (1.3%)

regimes4.0ms (0.3%)

derivations5.0ms (0.4%)

preprocess16.0ms (1.2%)

end0.0ms (0%)

Profiling