Metrics for sqrt B (should all be same)

start0.0ms (0%)

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

analyze1.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample1.0s (56.7%)

Memory

49.0MiB live, 1 027.1MiB allocated; 253ms collecting garbage

Samples

673.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 423.0ms

ival-mult: 289.0ms (68.3% of total)

ival-sqrt: 118.0ms (27.9% of total)

exact: 10.0ms (2.4% of total)

adjust: 3.0ms (0.7% of total)

ival-assert: 3.0ms (0.7% of total)

Bogosity

explain154.0ms (8.6%)

Memory

-2.9MiB live, 98.1MiB allocated; 14ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
137	-	1	(2.1978410373408023e-160)	`(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	74	0
↳	`(.f64 (.f64 #s(literal 2 binary64) x) x)`	overflow	74
`sqrt.f64`	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`	uflow-rescue	62	0
↳	`(.f64 (.f64 #s(literal 2 binary64) x) x)`	underflow	62

Confusion

	Predicted +	Predicted -
+	136	1
-	0	119

Precision

1.0

Recall

0.9927007299270073

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	136	0	1
-	0	0	119

Precision?

1.0

Recall?

0.9927007299270073

Freqs

test

number	freq
0	120
1	136

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

45.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-mult: 18.0ms (68.8% of total)

ival-sqrt: 6.0ms (22.9% of total)

ival-true: 1.0ms (3.8% of total)

exact: 1.0ms (3.8% of total)

adjust: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

preprocess325.0ms (18.2%)

Memory

-13.1MiB live, 130.1MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 0 (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
0	5	6
0	8	6
1	15	6
2	28	6
3	90	6
4	232	6
5	818	6
6	4263	6
0	8038	3

Stop Event

1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.2%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Compiler

Compiled 6 to 5 computations (16.7% saved)

series5.0ms (0.3%)

Memory

2.9MiB live, 2.9MiB 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
2.0ms	x	@	inf	((sqrt (* (* 2 x) x)) (* (* 2 x) x) (* 2 x) 2 x)
2.0ms	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)

rewrite39.0ms (2.2%)

Memory

21.8MiB live, 21.8MiB allocated; 0ms 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))))

eval35.0ms (2%)

Memory: -37.0MiB live, 9.2MiB allocated; 5ms collecting garbage
Compiler: Compiled 513 to 135 computations (73.7% saved)

prune3.0ms (0.2%)

Memory

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

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	56	4	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	4	61

Accuracy

100.0%

Counts

61 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	99.5%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
▶	50.2%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	99.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 27 to 21 computations (22.2% saved)

series8.0ms (0.4%)

Memory

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

Counts

13 → 17

Calls

Call 1

Inputs
#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)
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)
(hypot.f64 x x)

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

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	((sqrt (* (* 2 x) x)) (* (sqrt 2) x) (sqrt 2) 2 x (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (sqrt (+ (* x x) (* x x))))
2.0ms	x	@	inf	((sqrt (* (* 2 x) x)) (* (sqrt 2) x) (sqrt 2) 2 x (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (sqrt (+ (* x x) (* x x))))
1.0ms	x	@	0	((sqrt (* (* 2 x) x)) (* (sqrt 2) x) (sqrt 2) 2 x (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (sqrt (+ (* x x) (* x x))))

Time

Variable

Point

Expression

4.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

rewrite28.0ms (1.6%)

Memory

6.7MiB live, 6.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	226
0	73	179
0	162	179

Stop Event

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

Counts

30 → 116

Calls

Call 1

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

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

eval7.0ms (0.4%)

Memory: 6.3MiB live, 6.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 685 to 163 computations (76.2% saved)

prune5.0ms (0.3%)

Memory

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

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	77	5	82

Accuracy

100.0%

Counts

82 → 5

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))
✓	99.5%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
✓	50.2%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 35 to 27 computations (22.9% saved)

series4.0ms (0.2%)

Memory

4.1MiB live, 4.1MiB 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)

rewrite35.0ms (2%)

Memory

-32.9MiB live, 13.5MiB allocated; 4ms 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))))

eval2.0ms (0.1%)

Memory: 2.9MiB live, 2.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 241 to 53 computations (78% saved)

prune3.0ms (0.2%)

Memory

4.2MiB live, 4.2MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	24	5	29

Accuracy

100.0%

Counts

29 → 5

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))
✓	99.5%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
✓	50.2%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 76 to 49 computations (35.5% saved)

regimes7.0ms (0.4%)

Memory

8.9MiB live, 8.9MiB 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))
(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	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
2.0ms	(.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)

regimes7.0ms (0.4%)

Memory

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

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(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
99.5%	1	`(.f64 (.f64 #s(literal 2 binary64) x) x)`
99.5%	1	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
99.5%	1	`x`

Compiler

Compiled 12 to 10 computations (16.7% saved)

regimes5.0ms (0.3%)

Memory

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

Accuracy

Total -31.5b remaining (-6786.2%)

Threshold costs -31.5b (-6786.2%)

Counts

3 → 1

Calls

Call 1

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

Results

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

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify65.0ms (3.7%)

Memory

-13.8MiB live, 32.8MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	20	21
2	33	21
3	95	21
4	280	21
5	1777	21
6	6429	21

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations6.0ms (0.3%)

Memory

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

Stop Event

1×

done

Compiler

Compiled 21 to 14 computations (33.3% saved)

preprocess28.0ms (1.6%)

Memory: 26.3MiB live, 26.3MiB allocated; 0ms collecting garbage
Remove: (abs x)
Compiler: Compiled 60 to 42 computations (30% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze1.0ms (0%)

sample1.0s (56.7%)

explain154.0ms (8.6%)

preprocess325.0ms (18.2%)

eval0.0ms (0%)

prune0.0ms (0%)

series5.0ms (0.3%)

rewrite39.0ms (2.2%)

eval35.0ms (2%)

prune3.0ms (0.2%)

series8.0ms (0.4%)

rewrite28.0ms (1.6%)

eval7.0ms (0.4%)

prune5.0ms (0.3%)

series4.0ms (0.2%)

rewrite35.0ms (2%)

eval2.0ms (0.1%)

prune3.0ms (0.2%)

regimes7.0ms (0.4%)

regimes7.0ms (0.4%)

regimes5.0ms (0.3%)

simplify65.0ms (3.7%)

derivations6.0ms (0.3%)

preprocess28.0ms (1.6%)

end0.0ms (0%)

Profiling