Metrics for Linear.Quaternion:$clog from linear-1.19.1.3

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze23.0ms (2.9%)

Memory

-9.8MiB live, 28.0MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
62.5%	62.4%	37.5%	0.1%	0%	0%	0%	5
66.7%	62.4%	31.2%	0.1%	0%	6.2%	0%	6
75%	65.6%	21.9%	0.1%	0%	12.5%	0%	7
80%	68.7%	17.2%	0.1%	0%	14%	0%	8
85.7%	70.2%	11.7%	0.1%	0%	18%	0%	9
88.9%	71.8%	9%	0.1%	0%	19.1%	0%	10
92.3%	72.6%	6%	0.1%	0%	21.3%	0%	11
94.1%	73.4%	4.6%	0.1%	0%	22%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample600.0ms (75.6%)

Memory

13.7MiB live, 953.9MiB allocated

Samples

372.0ms	8 256×	0	valid
13.0ms	315×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 200.0ms

ival-mult: 71.0ms (35.5% of total)

ival-sqrt: 68.0ms (34% of total)

ival-add: 51.0ms (25.5% of total)

ival-true: 7.0ms (3.5% of total)

ival-assert: 4.0ms (2% of total)

Bogosity

explain60.0ms (7.5%)

Memory

7.9MiB live, 85.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
94	-	-	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
0	-	-	`(+.f64 (*.f64 x x) y)`
0	-	-	`y`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (*.f64 x x) y))`	oflow-rescue	94	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	94
↳	`(*.f64 x x)`	overflow	94

Confusion

	Predicted +	Predicted -
+	94	0
-	0	162

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	94	0	0
-	0	0	162

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	162
1	94

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 58 to 24 computations (58.6% saved)

Precisions

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

ival-sqrt: 5.0ms (42.3% of total)

ival-mult: 4.0ms (33.8% of total)

ival-add: 2.0ms (16.9% of total)

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

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

preprocess3.0ms (0.3%)

Memory

4.4MiB live, 4.4MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

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

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.7%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(+.f64 (*.f64 x x) y)
cost-diff	0	(sqrt.f64 (+.f64 (*.f64 x x) y))

Calls

Call 1

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

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

localize19.0ms (2.5%)

Memory

-34.3MiB live, 20.5MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (*.f64 x x) y)
accuracy	21.957160346264658	(sqrt.f64 (+.f64 (*.f64 x x) y))

Samples

11.0ms

256×

valid

Compiler

Compiled 34 to 12 computations (64.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 2.0ms (37.7% of total)

ival-sqrt: 2.0ms (37.7% of total)

ival-add: 1.0ms (18.8% of total)

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

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

series5.0ms (0.6%)

Memory

6.9MiB live, 6.9MiB allocated

Counts

3 → 28

Calls

Call 1

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

Outputs
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
y
(+ y (pow x 2))
(pow x 2)
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* y (+ 1 (/ (pow x 2) y)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))

Calls

6 calls:

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

simplify0.0ms (0.1%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Counts

28 → 3

Calls

Call 1

Inputs
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
y
(+ y (pow x 2))
(pow x 2)
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* y (+ 1 (/ (pow x 2) y)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))

Outputs
(sqrt y)
(sqrt.f64 (+.f64 (*.f64 x x) y))
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+.f64 (*.f64 x x) y)
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(*.f64 x x)

rewrite0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Counts

3 → 3

Calls

Call 1

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

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

eval1.0ms (0.1%)

Memory: 1.2MiB live, 1.2MiB allocated
Compiler: Compiled 53 to 11 computations (79.2% saved)

prune1.0ms (0.1%)

Memory

2.0MiB live, 2.0MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	4	2	6
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	4	3	7

Accuracy

65.7%

Counts

7 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	65.7%	(sqrt.f64 (+.f64 (*.f64 x x) y))
▶	6.7%	#s(approx (sqrt (+ (* x x) y)) (+.f64 (*.f64 x x) y))
▶	5.9%	#s(approx (sqrt (+ (* x x) y)) (*.f64 x x))

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(+.f64 (*.f64 x x) y)
cost-diff	0	#s(approx (sqrt (+ (* x x) y)) (+.f64 (*.f64 x x) y))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (sqrt (+ (* x x) y)) (*.f64 x x))

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) y)) (*.f64 x x))
(*.f64 x x)
x
#s(approx (sqrt (+ (* x x) y)) (+.f64 (*.f64 x x) y))
(+.f64 (*.f64 x x) y)
(*.f64 x x)
x
y

Outputs
#s(approx (sqrt (+ (* x x) y)) (*.f64 x x))
(*.f64 x x)
x
#s(approx (sqrt (+ (* x x) y)) (+.f64 (*.f64 x x) y))
(+.f64 (*.f64 x x) y)
(*.f64 x x)
x
y

localize17.0ms (2.1%)

Memory

22.7MiB live, 22.7MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (*.f64 x x) y)
accuracy	59.71322172754641	#s(approx (sqrt (+ (* x x) y)) (+.f64 (*.f64 x x) y))
accuracy	0.0	(*.f64 x x)
accuracy	60.24264412447722	#s(approx (sqrt (+ (* x x) y)) (*.f64 x x))

Samples

12.0ms

256×

valid

Compiler

Compiled 64 to 16 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 2.0ms (37.5% of total)

ival-sqrt: 2.0ms (37.5% of total)

ival-add: 1.0ms (18.7% of total)

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

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

series2.0ms (0.3%)

Memory

3.3MiB live, 3.3MiB allocated

Counts

4 → 28

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) y)) (*.f64 x x))
(*.f64 x x)
#s(approx (sqrt (+ (* x x) y)) (+.f64 (*.f64 x x) y))
(+.f64 (*.f64 x x) y)

Outputs
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(pow x 2)
y
(+ y (pow x 2))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* y (+ 1 (/ (pow x 2) y)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	((sqrt (+ (* x x) y)) (* x x) (sqrt (+ (* x x) y)) (+ (* x x) y))
0.0ms	x	@	-inf	((sqrt (+ (* x x) y)) (* x x) (sqrt (+ (* x x) y)) (+ (* x x) y))
0.0ms	y	@	-inf	((sqrt (+ (* x x) y)) (* x x) (sqrt (+ (* x x) y)) (+ (* x x) y))
0.0ms	x	@	0	((sqrt (+ (* x x) y)) (* x x) (sqrt (+ (* x x) y)) (+ (* x x) y))
0.0ms	y	@	inf	((sqrt (+ (* x x) y)) (* x x) (sqrt (+ (* x x) y)) (+ (* x x) y))

simplify2.0ms (0.2%)

Memory

-37.5MiB live, 0.8MiB allocated

Algorithm

1×	egg-herbie

Counts

28 → 4

Calls

Call 1

Inputs
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(pow x 2)
y
(+ y (pow x 2))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* y (+ 1 (/ (pow x 2) y)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))

Outputs
(sqrt y)
#s(approx (sqrt (+ (* x x) y)) (*.f64 x x))
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(*.f64 x x)
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (*.f64 x x) y))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(+.f64 (*.f64 x x) y)

rewrite0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Counts

4 → 4

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) y)) (*.f64 x x))
(*.f64 x x)
#s(approx (sqrt (+ (* x x) y)) (+.f64 (*.f64 x x) y))
(+.f64 (*.f64 x x) y)

Outputs
#s(approx (sqrt (+ (* x x) y)) (*.f64 x x))
(*.f64 x x)
#s(approx (sqrt (+ (* x x) y)) (+.f64 (*.f64 x x) y))
(+.f64 (*.f64 x x) y)

eval1.0ms (0.1%)

Memory: 1.2MiB live, 1.2MiB allocated
Compiler: Compiled 92 to 11 computations (88% saved)

prune2.0ms (0.3%)

Memory

3.5MiB live, 3.5MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	7	0	7
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	7	3	10

Accuracy

65.7%

Counts

10 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	65.7%	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	6.7%	#s(approx (sqrt (+ (* x x) y)) (+.f64 (*.f64 x x) y))
✓	5.9%	#s(approx (sqrt (+ (* x x) y)) (*.f64 x x))

Compiler

Compiled 56 to 30 computations (46.4% saved)

regimes9.0ms (1.1%)

Memory

15.7MiB live, 15.7MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) y)) (*.f64 x x))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (*.f64 x x) y))
(sqrt.f64 (+.f64 (*.f64 x x) y))

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

Calls

5 calls:

2.0ms	y
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
2.0ms	(+.f64 (*.f64 x x) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
65.7%	1	`x`
65.7%	1	`y`
65.7%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
65.7%	1	`(+.f64 (*.f64 x x) y)`
65.7%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes7.0ms (0.9%)

Memory

13.9MiB live, 13.9MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) y)) (*.f64 x x))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (*.f64 x x) y))

Outputs
#s(approx (sqrt (+ (* x x) y)) (+.f64 (*.f64 x x) y))

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
6.7%	1	`y`
6.7%	1	`x`
6.7%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
6.7%	1	`(+.f64 (*.f64 x x) y)`
6.7%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes6.0ms (0.8%)

Memory

-21.4MiB live, 17.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) y)) (*.f64 x x))

Outputs
#s(approx (sqrt (+ (* x x) y)) (*.f64 x x))

Calls

5 calls:

2.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	y
1.0ms	x
1.0ms	(+.f64 (*.f64 x x) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
5.9%	1	`x`
5.9%	1	`y`
5.9%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
5.9%	1	`(+.f64 (*.f64 x x) y)`
5.9%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

simplify4.0ms (0.5%)

Memory

11.5MiB live, 11.5MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (*.f64 x x) y))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x x))

Outputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (*.f64 x x) y))
#s(approx (sqrt (+ (* x x) y)) (*.f64 x x))

soundness1.0ms (0.1%)

Memory

1.1MiB live, 1.1MiB allocated

Stop Event

1×

done

Compiler

Compiled 28 to 10 computations (64.3% saved)

preprocess29.0ms (3.7%)

Memory: 10.9MiB live, 49.3MiB allocated
Compiler: Compiled 126 to 62 computations (50.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze23.0ms (2.9%)

sample600.0ms (75.6%)

explain60.0ms (7.5%)

preprocess3.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify0.0ms (0%)

localize19.0ms (2.5%)

series5.0ms (0.6%)

simplify0.0ms (0.1%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

simplify0.0ms (0%)

localize17.0ms (2.1%)

series2.0ms (0.3%)

simplify2.0ms (0.2%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune2.0ms (0.3%)

regimes9.0ms (1.1%)

regimes7.0ms (0.9%)

regimes6.0ms (0.8%)

simplify4.0ms (0.5%)

soundness1.0ms (0.1%)

preprocess29.0ms (3.7%)

end0.0ms (0%)

Profiling