Metrics for Data.Random.Distribution.Normal:normalTail from random-fu-0.2.6.2

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample598.0ms (56.5%)

Memory

18.7MiB live, 793.0MiB allocated; 255ms collecting garbage

Samples

367.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 136.0ms

ival-mult!: 81.0ms (59.6% of total)

ival-add!: 53.0ms (39% of total)

adjust: 2.0ms (1.5% of total)

Bogosity

explain57.0ms (5.4%)

Memory

41.3MiB live, 88.7MiB allocated; 5ms collecting garbage

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(+.f64 (*.f64 x x) y)`
-	-	`(+.f64 (+.f64 (*.f64 x x) y) y)`
-	-	`y`
-	-	`(*.f64 x x)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

17.0ms

512×

valid

Compiler

Compiled 45 to 19 computations (57.8% saved)

Precisions

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

ival-mult!: 3.0ms (55.9% of total)

ival-add!: 2.0ms (37.2% of total)

adjust: 0.0ms (0% of total)

preprocess109.0ms (10.3%)

Memory

-49.9MiB live, 50.6MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	48
1	48	45
2	122	43
3	199	42
4	309	42
5	379	42
6	587	42
7	1378	42
8	6105	42

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)

Symmetry

(abs x)

Compiler

Compiled 14 to 10 computations (28.6% saved)

series4.0ms (0.4%)

Memory

6.8MiB live, 6.8MiB allocated; 0ms collecting garbage

Counts

5 → 15

Calls

Call 1

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

Outputs
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* 2 y)))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (+ (* 2 y) (pow x 2))))
#s(approx (+ (* x x) y) #s(hole binary64 y))
#s(approx (+ (* x x) y) #s(hole binary64 (+ y (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (pow x 2)))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))))
#s(approx (+ (* x x) y) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) y) #s(hole binary64 (* (pow x 2) (+ 1 (/ y (pow x 2))))))
#s(approx y #s(hole binary64 y))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* y (+ 2 (/ (pow x 2) y)))))
#s(approx (+ (* x x) y) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y)))))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))))
#s(approx (+ (* x x) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))))

Calls

6 calls:

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

rewrite77.0ms (7.3%)

Memory

41.4MiB live, 86.1MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	204
0	52	200
1	231	200
0	1992	181

Stop Event

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

Counts

20 → 133

Calls

Call 1

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

Outputs
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 y y) #s(literal 4 binary64))) (-.f64 (.f64 x x) (+.f64 y y)))
(/.f64 (-.f64 (.f64 y y) (.f64 (fma.f64 x x y) (fma.f64 x x y))) (-.f64 y (fma.f64 x x y)))
(/.f64 (neg.f64 (.f64 (+.f64 (fma.f64 x x y) y) (+.f64 y (-.f64 y (.f64 x x))))) (neg.f64 (+.f64 y (-.f64 y (*.f64 x x)))))
(/.f64 (neg.f64 (*.f64 (+.f64 (fma.f64 x x y) y) (-.f64 (fma.f64 x x y) y))) (neg.f64 (-.f64 (fma.f64 x x y) y)))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x) (.f64 (.f64 (.f64 y y) y) #s(literal 8 binary64)))) (neg.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 (.f64 x x) (-.f64 (*.f64 x x) (+.f64 y y))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (fma.f64 x x y) (.f64 (.f64 y y) y))) (neg.f64 (fma.f64 (fma.f64 x x y) (fma.f64 x x y) (.f64 y (-.f64 y (fma.f64 x x y))))))
(/.f64 (.f64 (+.f64 (fma.f64 x x y) y) (+.f64 y (-.f64 y (.f64 x x)))) (+.f64 y (-.f64 y (*.f64 x x))))
(/.f64 (*.f64 (+.f64 (fma.f64 x x y) y) (-.f64 (fma.f64 x x y) y)) (-.f64 (fma.f64 x x y) y))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x) (.f64 (.f64 (.f64 y y) y) #s(literal 8 binary64))) (fma.f64 (.f64 (.f64 x x) x) x (-.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) (.f64 (*.f64 (+.f64 y y) x) x))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x) (.f64 (.f64 (.f64 y y) y) #s(literal 8 binary64))) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 (.f64 x x) (-.f64 (*.f64 x x) (+.f64 y y)))))
(/.f64 (fma.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (fma.f64 x x y) (.f64 (.f64 y y) y)) (fma.f64 y y (-.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (*.f64 (fma.f64 x x y) y))))
(/.f64 (fma.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (fma.f64 x x y) (.f64 (.f64 y y) y)) (fma.f64 (fma.f64 x x y) (fma.f64 x x y) (.f64 y (-.f64 y (fma.f64 x x y)))))
(fma.f64 (.f64 (neg.f64 x) #s(literal 1 binary64)) (.f64 (neg.f64 x) #s(literal 1 binary64)) (+.f64 y y))
(fma.f64 (.f64 (fabs.f64 x) #s(literal 1 binary64)) (.f64 (fabs.f64 x) #s(literal 1 binary64)) (+.f64 y y))
(fma.f64 (.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64)) (+.f64 y y))
(fma.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (.f64 #s(literal 1 binary64) (neg.f64 x)) (+.f64 y y))
(fma.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x) (+.f64 y y))
(fma.f64 (.f64 #s(literal 1 binary64) (fabs.f64 x)) (.f64 #s(literal 1 binary64) (fabs.f64 x)) (+.f64 y y))
(fma.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x) (+.f64 y y))
(fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) (+.f64 y y))
(fma.f64 (*.f64 #s(literal 1 binary64) x) x (+.f64 y y))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (+.f64 y y))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (+.f64 y y))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (+.f64 y y))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (+.f64 y y))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1 binary64)) (+.f64 y y))
(fma.f64 (neg.f64 x) (neg.f64 x) (+.f64 y y))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 1 binary64)) (+.f64 y y))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (+.f64 y y))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) (+.f64 y y))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) (+.f64 y y))
(fma.f64 #s(literal 2 binary64) y (*.f64 x x))
(fma.f64 y #s(literal 2 binary64) (*.f64 x x))
(fma.f64 x (*.f64 x #s(literal 1 binary64)) (+.f64 y y))
(fma.f64 x x (+.f64 y y))
(-.f64 (/.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) (+.f64 y (-.f64 y (.f64 x x)))) (/.f64 (.f64 (.f64 (.f64 x x) x) x) (+.f64 y (-.f64 y (*.f64 x x)))))
(-.f64 (/.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (-.f64 (fma.f64 x x y) y)) (/.f64 (.f64 y y) (-.f64 (fma.f64 x x y) y)))
(-.f64 (.f64 x x) (.f64 #s(literal -2 binary64) y))
(-.f64 (.f64 x x) (.f64 (neg.f64 y) #s(literal 2 binary64)))
(-.f64 (+.f64 y y) (*.f64 (neg.f64 x) x))
(+.f64 (/.f64 (.f64 (.f64 (.f64 y y) y) #s(literal 8 binary64)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 (.f64 x x) (-.f64 (.f64 x x) (+.f64 y y))))) (/.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 (.f64 x x) (-.f64 (.f64 x x) (+.f64 y y))))))
(+.f64 (/.f64 (.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (fma.f64 x x y)) (fma.f64 (fma.f64 x x y) (fma.f64 x x y) (.f64 y (-.f64 y (fma.f64 x x y))))) (/.f64 (.f64 (.f64 y y) y) (fma.f64 (fma.f64 x x y) (fma.f64 x x y) (.f64 y (-.f64 y (fma.f64 x x y))))))
(+.f64 (*.f64 x x) (+.f64 y y))
(+.f64 (+.f64 y y) (*.f64 x x))
(+.f64 (fma.f64 x x y) y)
(+.f64 y (fma.f64 x x y))
(/.f64 (neg.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y))) (neg.f64 (-.f64 (*.f64 x x) y)))
(/.f64 (neg.f64 (.f64 (fma.f64 x x y) (-.f64 y (.f64 x x)))) (neg.f64 (-.f64 y (*.f64 x x))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y))) (neg.f64 (fma.f64 (.f64 (.f64 x x) x) x (.f64 y (-.f64 y (.f64 x x))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y))) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
(/.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)) (-.f64 (*.f64 x x) y))
(/.f64 (.f64 (fma.f64 x x y) (-.f64 y (.f64 x x))) (-.f64 y (*.f64 x x)))
(/.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) (fma.f64 (.f64 (.f64 x x) x) x (.f64 y (-.f64 y (.f64 x x)))))
(/.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))
(fma.f64 (.f64 (neg.f64 x) #s(literal 1 binary64)) (.f64 (neg.f64 x) #s(literal 1 binary64)) y)
(fma.f64 (.f64 (fabs.f64 x) #s(literal 1 binary64)) (.f64 (fabs.f64 x) #s(literal 1 binary64)) y)
(fma.f64 (.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64)) y)
(fma.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (.f64 #s(literal 1 binary64) (neg.f64 x)) y)
(fma.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x) y)
(fma.f64 (.f64 #s(literal 1 binary64) (fabs.f64 x)) (.f64 #s(literal 1 binary64) (fabs.f64 x)) y)
(fma.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x) y)
(fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) y)
(fma.f64 (*.f64 #s(literal 1 binary64) x) x y)
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) y)
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) y)
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) y)
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) y)
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1 binary64)) y)
(fma.f64 (neg.f64 x) (neg.f64 x) y)
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 1 binary64)) y)
(fma.f64 (fabs.f64 x) (fabs.f64 x) y)
(fma.f64 #s(literal 1 binary64) (*.f64 x x) y)
(fma.f64 (*.f64 x x) #s(literal 1 binary64) y)
(fma.f64 x (*.f64 x #s(literal 1 binary64)) y)
(fma.f64 x x y)
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) x) x) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))
(-.f64 (/.f64 (.f64 y y) (-.f64 y (.f64 x x))) (/.f64 (.f64 (.f64 (.f64 x x) x) x) (-.f64 y (.f64 x x))))
(-.f64 y (*.f64 (neg.f64 x) x))
(+.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (fma.f64 (.f64 (.f64 x x) x) x (.f64 y (-.f64 y (.f64 x x))))) (/.f64 (.f64 (.f64 y y) y) (fma.f64 (.f64 (.f64 x x) x) x (.f64 y (-.f64 y (*.f64 x x))))))
(+.f64 (/.f64 (.f64 (.f64 y y) y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (/.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
(+.f64 (*.f64 x x) y)
(+.f64 y (*.f64 x x))
(.f64 (.f64 (neg.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 x) #s(literal 1 binary64)))
(.f64 (.f64 (fabs.f64 x) #s(literal 1 binary64)) (*.f64 (fabs.f64 x) #s(literal 1 binary64)))
(.f64 (.f64 x #s(literal 1 binary64)) (*.f64 x #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (*.f64 #s(literal 1 binary64) (neg.f64 x)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 x)) (*.f64 #s(literal 1 binary64) (fabs.f64 x)))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x))
(.f64 (.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 1 binary64) x))
(.f64 (.f64 #s(literal 1 binary64) x) x)
(*.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) (.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) #s(literal 1 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 x (.f64 x #s(literal 1 binary64)))
(*.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))
(/.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) #s(literal 0 binary64)))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(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
y
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))
#s(approx (+ (+ (* x x) y) y) (+.f64 (fma.f64 x x y) y))
#s(approx (+ (* x x) y) y)
#s(approx (+ (* x x) y) (fma.f64 x x y))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (+ (+ (* x x) y) y) (*.f64 x x))
#s(approx (+ (+ (* x x) y) y) (.f64 (.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal 2 binary64) #s(literal 1 binary64)) x) x))
#s(approx (+ (* x x) y) (*.f64 x x))
#s(approx (+ (* x x) y) (.f64 (.f64 (-.f64 (/.f64 y (*.f64 x x)) #s(literal -1 binary64)) x) x))
#s(approx y y)
#s(approx (+ (+ (* x x) y) y) (*.f64 (fma.f64 x (/.f64 x y) #s(literal 2 binary64)) y))
#s(approx (+ (* x x) y) (fma.f64 (/.f64 (*.f64 x x) y) y y))
#s(approx (+ (+ (* x x) y) y) (.f64 (neg.f64 y) (-.f64 (/.f64 (.f64 (neg.f64 x) x) y) #s(literal 2 binary64))))
#s(approx (+ (* x x) y) (.f64 (neg.f64 y) (-.f64 (/.f64 (.f64 (neg.f64 x) x) y) #s(literal 1 binary64))))

eval21.0ms (2%)

Memory: -25.2MiB live, 20.9MiB allocated; 5ms collecting garbage
Compiler: Compiled 1 921 to 371 computations (80.7% saved)

prune4.0ms (0.4%)

Memory

6.8MiB live, 6.8MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	127	4	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	4	132

Accuracy

100.0%

Counts

132 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 x x (+.f64 y y))
▶	59.5%	(+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y)
▶	50.8%	(+.f64 #s(approx (+ (* x x) y) y) y)
▶	52.0%	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Compiler

Compiled 37 to 24 computations (35.1% saved)

series4.0ms (0.4%)

Memory

6.3MiB live, 6.3MiB allocated; 0ms collecting garbage

Counts

10 → 22

Calls

Call 1

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

Outputs
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* 2 y)))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (+ (* 2 y) (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (* x x) y) #s(hole binary64 y))
#s(approx (+ (* x x) y) #s(hole binary64 (+ y (pow x 2))))
#s(approx (+ (* x x) (+ y y)) #s(hole binary64 (* 2 y)))
#s(approx (+ (* x x) (+ y y)) #s(hole binary64 (+ (* 2 y) (pow x 2))))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (pow x 2)))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))))
#s(approx (+ (* x x) y) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) y) #s(hole binary64 (* (pow x 2) (+ 1 (/ y (pow x 2))))))
#s(approx (+ (* x x) (+ y y)) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) (+ y y)) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))))
#s(approx y #s(hole binary64 y))
#s(approx (+ y y) #s(hole binary64 (* 2 y)))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* y (+ 2 (/ (pow x 2) y)))))
#s(approx (+ (* x x) y) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y)))))
#s(approx (+ (* x x) (+ y y)) #s(hole binary64 (* y (+ 2 (/ (pow x 2) y)))))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))))
#s(approx (+ (* x x) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))))
#s(approx (+ (* x x) (+ y y)) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((+ (+ (* x x) y) y) (* x x) x (+ (+ (* x x) y) y) (+ (* x x) y) y (+ (+ (* x x) y) y) (+ (* x x) y) (+ (* x x) (+ y y)) (+ y y))
1.0ms	y	@	-inf	((+ (+ (* x x) y) y) (* x x) x (+ (+ (* x x) y) y) (+ (* x x) y) y (+ (+ (* x x) y) y) (+ (* x x) y) (+ (* x x) (+ y y)) (+ y y))
1.0ms	x	@	inf	((+ (+ (* x x) y) y) (* x x) x (+ (+ (* x x) y) y) (+ (* x x) y) y (+ (+ (* x x) y) y) (+ (* x x) y) (+ (* x x) (+ y y)) (+ y y))
1.0ms	y	@	inf	((+ (+ (* x x) y) y) (* x x) x (+ (+ (* x x) y) y) (+ (* x x) y) y (+ (+ (* x x) y) y) (+ (* x x) y) (+ (* x x) (+ y y)) (+ y y))
0.0ms	x	@	0	((+ (+ (* x x) y) y) (* x x) x (+ (+ (* x x) y) y) (+ (* x x) y) y (+ (+ (* x x) y) y) (+ (* x x) y) (+ (* x x) (+ y y)) (+ y y))

rewrite41.0ms (3.9%)

Memory

-20.0MiB live, 33.9MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	345
0	66	330
0	290	317

Stop Event

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

Counts

32 → 62

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) y) y) (*.f64 x x))
(*.f64 x x)
x
(+.f64 #s(approx (+ (* x x) y) y) y)
#s(approx (+ (* x x) y) y)
y
(+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y)
#s(approx (+ (* x x) y) (*.f64 x x))
(fma.f64 x x (+.f64 y y))
(+.f64 y y)
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* 2 y)))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (+ (* 2 y) (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (* x x) y) #s(hole binary64 y))
#s(approx (+ (* x x) y) #s(hole binary64 (+ y (pow x 2))))
#s(approx (+ (* x x) (+ y y)) #s(hole binary64 (* 2 y)))
#s(approx (+ (* x x) (+ y y)) #s(hole binary64 (+ (* 2 y) (pow x 2))))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (pow x 2)))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))))
#s(approx (+ (* x x) y) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) y) #s(hole binary64 (* (pow x 2) (+ 1 (/ y (pow x 2))))))
#s(approx (+ (* x x) (+ y y)) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) (+ y y)) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))))
#s(approx y #s(hole binary64 y))
#s(approx (+ y y) #s(hole binary64 (* 2 y)))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* y (+ 2 (/ (pow x 2) y)))))
#s(approx (+ (* x x) y) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y)))))
#s(approx (+ (* x x) (+ y y)) #s(hole binary64 (* y (+ 2 (/ (pow x 2) y)))))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))))
#s(approx (+ (* x x) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))))
#s(approx (+ (* x x) (+ y y)) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))))

Outputs
#s(approx (+ (+ (* x x) y) y) (*.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
(/.f64 (-.f64 (.f64 #s(approx (+ ( x x) y) y) #s(approx (+ (* x x) y) y)) (.f64 y y)) (-.f64 #s(approx (+ ( x x) y) y) y))
(/.f64 (+.f64 (pow.f64 #s(approx (+ (* x x) y) y) #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 #s(approx (+ (* x x) y) y) #s(approx (+ (* x x) y) y) (-.f64 (.f64 y y) (.f64 #s(approx (+ (* x x) y) y) y))))
(+.f64 #s(approx (+ (* x x) y) y) y)
(+.f64 y #s(approx (+ (* x x) y) y))
#s(approx (+ (* x x) y) y)
y
(/.f64 (-.f64 (.f64 #s(approx (+ ( x x) y) (.f64 x x)) #s(approx (+ ( x x) y) (.f64 x x))) (.f64 y y)) (-.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y))
(/.f64 (+.f64 (pow.f64 #s(approx (+ (* x x) y) (.f64 x x)) #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 #s(approx (+ ( x x) y) (.f64 x x)) #s(approx (+ ( x x) y) (.f64 x x)) (-.f64 (.f64 y y) (.f64 #s(approx (+ ( x x) y) (*.f64 x x)) y))))
(+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y)
(+.f64 y #s(approx (+ (* x x) y) (*.f64 x x)))
#s(approx (+ (* x x) y) (*.f64 x x))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (+.f64 y y) (+.f64 y y))) (-.f64 (*.f64 x x) (+.f64 y y)))
(/.f64 (-.f64 (.f64 (+.f64 y y) (+.f64 y y)) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (+.f64 y y) (*.f64 x x)))
(/.f64 (-.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (.f64 y y)) (-.f64 (fma.f64 x x y) y))
(/.f64 (+.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) (pow.f64 (+.f64 y y) #s(literal 3 binary64))) (fma.f64 (.f64 x x) (.f64 x x) (-.f64 (.f64 (+.f64 y y) (+.f64 y y)) (.f64 (.f64 x x) (+.f64 y y)))))
(/.f64 (+.f64 (pow.f64 (+.f64 y y) #s(literal 3 binary64)) (pow.f64 (.f64 x x) #s(literal 3 binary64))) (fma.f64 (+.f64 y y) (+.f64 y y) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (+.f64 y y) (.f64 x x)))))
(/.f64 (+.f64 (pow.f64 (fma.f64 x x y) #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (fma.f64 x x y) (fma.f64 x x y) (-.f64 (.f64 y y) (.f64 (fma.f64 x x y) y))))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (+.f64 y y))
(fma.f64 (neg.f64 x) (neg.f64 x) (+.f64 y y))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (+.f64 y y))
(fma.f64 #s(literal 2 binary64) y (*.f64 x x))
(fma.f64 y #s(literal 2 binary64) (*.f64 x x))
(fma.f64 x x (+.f64 y y))
(+.f64 (*.f64 x x) (+.f64 y y))
(+.f64 (+.f64 y y) (*.f64 x x))
(+.f64 (fma.f64 x x y) y)
(+.f64 y (fma.f64 x x y))
(*.f64 #s(literal 2 binary64) y)
(*.f64 y #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 y y) (.f64 y y)) (-.f64 y y))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y y (-.f64 (.f64 y y) (.f64 y y))))
(+.f64 y y)
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))
#s(approx (+ (+ (* x x) y) y) (fma.f64 x x (+.f64 y y)))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (+ (* x x) y) y)
#s(approx (+ (* x x) y) (fma.f64 x x y))
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))
#s(approx (+ (+ (* x x) y) y) (fma.f64 x x (+.f64 y y)))
#s(approx (+ (+ (* x x) y) y) (*.f64 x x))
#s(approx (+ (+ (* x x) y) y) (.f64 (fma.f64 (/.f64 y (.f64 x x)) #s(literal 2 binary64) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (+ (* x x) y) (*.f64 x x))
#s(approx (+ (* x x) y) (.f64 (+.f64 (/.f64 y (.f64 x x)) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (+ (+ (* x x) y) y) (*.f64 x x))
#s(approx (+ (+ (* x x) y) y) (.f64 (fma.f64 (/.f64 y (.f64 x x)) #s(literal 2 binary64) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx y y)
#s(approx (+ y y) (+.f64 y y))
#s(approx (+ (+ (* x x) y) y) (.f64 (+.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) y))
#s(approx (+ (* x x) y) (.f64 (+.f64 (/.f64 (.f64 x x) y) #s(literal 1 binary64)) y))
#s(approx (+ (+ (* x x) y) y) (.f64 (+.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) y))
#s(approx (+ (+ (* x x) y) y) (neg.f64 (.f64 (-.f64 (neg.f64 (/.f64 (.f64 x x) y)) #s(literal 2 binary64)) y)))
#s(approx (+ (* x x) y) (neg.f64 (.f64 (-.f64 (neg.f64 (/.f64 (.f64 x x) y)) #s(literal 1 binary64)) y)))
#s(approx (+ (+ (* x x) y) y) (neg.f64 (.f64 (-.f64 (neg.f64 (/.f64 (.f64 x x) y)) #s(literal 2 binary64)) y)))

eval5.0ms (0.5%)

Memory: 8.7MiB live, 8.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 888 to 171 computations (80.7% saved)

prune3.0ms (0.3%)

Memory

5.6MiB live, 5.6MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	58	4	62

Accuracy

100.0%

Counts

62 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x x (+.f64 y y))
✓	59.5%	(+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y)
✓	50.8%	(+.f64 #s(approx (+ (* x x) y) y) y)
✓	52.0%	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Compiler

Compiled 81 to 39 computations (51.9% saved)

regimes8.0ms (0.8%)

Memory

12.4MiB live, 12.4MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

Outputs
(fma.f64 x x (+.f64 y y))

Calls

4 calls:

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

Results

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

Compiler

Compiled 12 to 12 computations (0% saved)

regimes13.0ms (1.3%)

Memory

-35.0MiB live, 11.9MiB allocated; 2ms collecting garbage

Counts

3 → 2

Calls

Call 1

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

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

Calls

4 calls:

8.0ms	x
2.0ms	y
2.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
88.6%	2	`(*.f64 x x)`
82.3%	2	`(+.f64 (+.f64 (*.f64 x x) y) y)`
88.6%	2	`x`
66.8%	3	`y`

Compiler

Compiled 12 to 12 computations (0% saved)

regimes3.0ms (0.2%)

Memory

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

Counts

2 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
87.1%	2	`(*.f64 x x)`
87.1%	2	`x`

Compiler

Compiled 4 to 5 computations (-25% saved)

regimes4.0ms (0.4%)

Memory

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

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
50.8%	1	`y`
50.8%	1	`(+.f64 (+.f64 (*.f64 x x) y) y)`
50.8%	1	`(*.f64 x x)`
50.8%	1	`x`

Compiler

Compiled 12 to 12 computations (0% saved)

bsearch9.0ms (0.8%)

Memory

6.1MiB live, 6.1MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	7.191168370137037e-70	9.731570422971526e-66

Samples

4.0ms

128×

valid

Compiler

Compiled 170 to 130 computations (23.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-add!: 1.0ms (79.6% of total)

ival-mult!: 1.0ms (79.6% of total)

adjust: 0.0ms (0% of total)

bsearch8.0ms (0.7%)

Memory

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

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
7.0ms	1.3713736895211596e-7	1.4945144987779612e-5

Samples

3.0ms

112×

valid

Compiler

Compiled 150 to 115 computations (23.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-mult!: 1.0ms (91.6% of total)

adjust: 0.0ms (0% of total)

ival-add!: 0.0ms (0% of total)

derivations31.0ms (3%)

Memory

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

Stop Event

1×

done

Compiler

Compiled 63 to 19 computations (69.8% saved)

preprocess59.0ms (5.6%)

Memory: 0.8MiB live, 47.2MiB allocated; 4ms collecting garbage
Remove: (abs x)
Compiler: Compiled 266 to 116 computations (56.4% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample598.0ms (56.5%)

explain57.0ms (5.4%)

preprocess109.0ms (10.3%)

series4.0ms (0.4%)

rewrite77.0ms (7.3%)

eval21.0ms (2%)

prune4.0ms (0.4%)

series4.0ms (0.4%)

rewrite41.0ms (3.9%)

eval5.0ms (0.5%)

prune3.0ms (0.3%)

regimes8.0ms (0.8%)

regimes13.0ms (1.3%)

regimes3.0ms (0.2%)

regimes4.0ms (0.4%)

bsearch9.0ms (0.8%)

bsearch8.0ms (0.7%)

derivations31.0ms (3%)

preprocess59.0ms (5.6%)

end0.0ms (0%)

Profiling