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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

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

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	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)

sample1.2s (46.7%)

Memory

6.3MiB live, 1 234.0MiB allocated; 275ms collecting garbage

Samples

791.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 323.0ms

ival-add: 205.0ms (63.5% of total)

ival-mult: 105.0ms (32.5% of total)

ival-true: 7.0ms (2.2% of total)

adjust: 3.0ms (0.9% of total)

ival-assert: 3.0ms (0.9% of total)

Bogosity

explain88.0ms (3.5%)

Memory

4.2MiB live, 181.4MiB allocated; 43ms 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

25.0ms

512×

valid

Compiler

Compiled 45 to 19 computations (57.8% saved)

Precisions

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

ival-add: 9.0ms (67.7% of total)

ival-mult: 4.0ms (30.1% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess233.0ms (9.3%)

Memory

34.2MiB live, 220.3MiB allocated; 61ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	47	38
2	121	36
3	198	35
4	312	35
5	382	35
6	590	35
7	1382	35
8	6127	35
0	5	7
0	8	7
1	16	7
2	38	7
3	82	7
4	117	7
5	155	7
6	247	7
7	608	7
8	2900	7
0	8274	6

Stop Event

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

Calls

Call 1

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

Outputs
(+.f64 (+.f64 (*.f64 x x) y) y)
(fma.f64 #s(literal 2 binary64) y (*.f64 x x))

Symmetry

(abs x)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

series4.0ms (0.2%)

Memory

8.3MiB live, 8.3MiB allocated; 0ms collecting garbage

Counts

5 → 12

Calls

Call 1

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

Outputs
(* 2 y)
(+ (* 2 y) (pow x 2))
y
(+ y (pow x 2))
(pow x 2)
x
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -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)

simplify227.0ms (9%)

Memory

-17.8MiB live, 270.8MiB allocated; 120ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	56
1	82	56
2	243	56
3	1101	56
4	6053	56
0	8213	48

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 10

Calls

Call 1

Inputs
(* 2 y)
(+ (* 2 y) (pow x 2))
y
(+ y (pow x 2))
(pow x 2)
x
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))

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

rewrite41.0ms (1.6%)

Memory

26.7MiB live, 117.9MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	17
0	8	17
1	41	17
0	356	15

Stop Event

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

Counts

5 → 59

Calls

Call 1

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

Outputs
(/.f64 (-.f64 (*.f64 y y) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64))) (-.f64 y (fma.f64 x x y)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 #s(literal 2 binary64) y) (.f64 #s(literal 2 binary64) y))) (-.f64 (.f64 x x) (*.f64 #s(literal 2 binary64) y)))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) y) #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 (.f64 #s(literal 2 binary64) y) (.f64 #s(literal 2 binary64) y)) (.f64 (.f64 x x) (*.f64 #s(literal 2 binary64) y)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (*.f64 y y))) (neg.f64 (-.f64 (fma.f64 x x y) y)))
(/.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 3 binary64)))) (neg.f64 (fma.f64 y (-.f64 y (fma.f64 x x y)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (*.f64 y y)) (-.f64 (fma.f64 x x y) y))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 3 binary64))) (fma.f64 y y (-.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (*.f64 (fma.f64 x x y) y))))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 3 binary64))) (fma.f64 y (-.f64 y (fma.f64 x x y)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64))))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) y))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (*.f64 #s(literal 2 binary64) y))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (*.f64 #s(literal 2 binary64) y))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (*.f64 #s(literal 2 binary64) y))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 #s(literal 2 binary64) y))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 #s(literal 2 binary64) y))
(fma.f64 #s(literal 2 binary64) y (*.f64 x x))
(fma.f64 x x (*.f64 #s(literal 2 binary64) y))
(-.f64 (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (-.f64 (fma.f64 x x y) y)) (/.f64 (*.f64 y y) (-.f64 (fma.f64 x x y) y)))
(+.f64 (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 3 binary64)) (fma.f64 y (-.f64 y (fma.f64 x x y)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (-.f64 y (fma.f64 x x y)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))))
(+.f64 (.f64 #s(literal 2 binary64) y) (.f64 x x))
(+.f64 (fma.f64 x x y) y)
(+.f64 y (fma.f64 x x y))
(+.f64 (.f64 x x) (.f64 #s(literal 2 binary64) y))
(/.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64))) (-.f64 y (.f64 x x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 y y))) (neg.f64 (-.f64 (.f64 x x) y)))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (fma.f64 y (-.f64 y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 y y)) (-.f64 (.f64 x x) y))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y y (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 y (.f64 x x)))))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y (-.f64 y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) 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 (neg.f64 x) (neg.f64 x) y)
(fma.f64 (fabs.f64 x) (fabs.f64 x) y)
(fma.f64 x x y)
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (*.f64 x x) y)))
(-.f64 y (*.f64 (neg.f64 (neg.f64 x)) (neg.f64 x)))
(-.f64 y (*.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 x)))
(-.f64 y (*.f64 (neg.f64 x) x))
(-.f64 y (*.f64 x (neg.f64 x)))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 y (-.f64 y (.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (-.f64 y (.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 y (*.f64 x x))
(+.f64 (*.f64 x x) y)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 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 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(neg.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
x
y

eval12.0ms (0.5%)

Memory: -28.4MiB live, 25.0MiB allocated; 4ms collecting garbage
Compiler: Compiled 816 to 181 computations (77.8% saved)

prune2.0ms (0.1%)

Memory

6.9MiB live, 6.9MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	2	66

Accuracy

100.0%

Counts

66 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (fma.f64 x x y) y)
▶	51.2%	#s(approx (+ (+ (* x x) y) y) (*.f64 #s(literal 2 binary64) y))

Compiler

Compiled 17 to 12 computations (29.4% saved)

series3.0ms (0.1%)

Memory

9.0MiB live, 9.0MiB allocated; 0ms collecting garbage

Counts

7 → 12

Calls

Call 1

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

Outputs
(* 2 y)
(+ (* 2 y) (pow x 2))
y
(+ y (pow x 2))
x
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	((+ (+ (* x x) y) y) (* 2 y) 2 y (+ (+ (* x x) y) y) (+ (* x x) y) x)
1.0ms	y	@	inf	((+ (+ (* x x) y) y) (* 2 y) 2 y (+ (+ (* x x) y) y) (+ (* x x) y) x)
0.0ms	x	@	-inf	((+ (+ (* x x) y) y) (* 2 y) 2 y (+ (+ (* x x) y) y) (+ (* x x) y) x)
0.0ms	x	@	inf	((+ (+ (* x x) y) y) (* 2 y) 2 y (+ (+ (* x x) y) y) (+ (* x x) y) x)
0.0ms	y	@	0	((+ (+ (* x x) y) y) (* 2 y) 2 y (+ (+ (* x x) y) y) (+ (* x x) y) x)

simplify162.0ms (6.4%)

Memory

-3.0MiB live, 223.0MiB allocated; 41ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	56
1	82	56
2	243	56
3	1101	56
4	6053	56
0	8213	48

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 10

Calls

Call 1

Inputs
(* 2 y)
(+ (* 2 y) (pow x 2))
y
(+ y (pow x 2))
x
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))

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

rewrite40.0ms (1.6%)

Memory

10.9MiB live, 56.1MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
0	12	26
1	47	26
0	380	26

Stop Event

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

Counts

7 → 61

Calls

Call 1

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

Outputs
#s(approx (+ (+ (* x x) y) y) (*.f64 #s(literal 2 binary64) 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))))
(fma.f64 #s(literal 1 binary64) y (*.f64 #s(literal 1 binary64) y))
(fma.f64 y #s(literal 1 binary64) (*.f64 y #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) y) (.f64 #s(literal 1 binary64) y))
(+.f64 (.f64 y #s(literal 1 binary64)) (.f64 y #s(literal 1 binary64)))
(+.f64 y y)
#s(literal 2 binary64)
y
(/.f64 (-.f64 (*.f64 y y) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64))) (-.f64 y (fma.f64 x x y)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 #s(literal 2 binary64) y) (.f64 #s(literal 2 binary64) y))) (-.f64 (.f64 x x) (*.f64 #s(literal 2 binary64) y)))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) y) #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 (.f64 #s(literal 2 binary64) y) (.f64 #s(literal 2 binary64) y)) (.f64 (.f64 x x) (*.f64 #s(literal 2 binary64) y)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (*.f64 y y))) (neg.f64 (-.f64 (fma.f64 x x y) y)))
(/.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 3 binary64)))) (neg.f64 (fma.f64 y (-.f64 y (fma.f64 x x y)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (*.f64 y y)) (-.f64 (fma.f64 x x y) y))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 3 binary64))) (fma.f64 y y (-.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (*.f64 (fma.f64 x x y) y))))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 3 binary64))) (fma.f64 y (-.f64 y (fma.f64 x x y)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64))))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (*.f64 #s(literal 2 binary64) y))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (*.f64 #s(literal 2 binary64) y))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (*.f64 #s(literal 2 binary64) y))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) y))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) x (*.f64 #s(literal 2 binary64) y))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 #s(literal 2 binary64) y))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 #s(literal 2 binary64) 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 #s(literal 2 binary64) y))
(-.f64 (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (-.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 (pow.f64 (fma.f64 x x y) #s(literal 3 binary64)) (fma.f64 y (-.f64 y (fma.f64 x x y)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (-.f64 y (fma.f64 x x y)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))))
(+.f64 (fma.f64 x x y) y)
(+.f64 (.f64 #s(literal 2 binary64) y) (.f64 x x))
(+.f64 y (fma.f64 x x y))
(+.f64 (.f64 x x) (.f64 #s(literal 2 binary64) y))
(/.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64))) (-.f64 y (.f64 x x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 y y))) (neg.f64 (-.f64 (.f64 x x) y)))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (fma.f64 y (-.f64 y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 y y)) (-.f64 (.f64 x x) y))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y y (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 y (.f64 x x)))))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y (-.f64 y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(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 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) y)
(fma.f64 (pow.f64 x #s(literal 1 binary64)) x y)
(fma.f64 (neg.f64 x) (neg.f64 x) y)
(fma.f64 (fabs.f64 x) (fabs.f64 x) y)
(fma.f64 x x y)
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (*.f64 x x) y)))
(-.f64 y (*.f64 (neg.f64 (neg.f64 x)) (neg.f64 x)))
(-.f64 y (*.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 x)))
(-.f64 y (*.f64 (neg.f64 x) x))
(-.f64 y (*.f64 x (neg.f64 x)))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 y (-.f64 y (.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (-.f64 y (.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 y (*.f64 x x))
(+.f64 (*.f64 x x) y)
x

eval6.0ms (0.2%)

Memory: 17.6MiB live, 17.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 880 to 170 computations (80.7% saved)

prune6.0ms (0.2%)

Memory

-37.5MiB live, 8.4MiB allocated; 7ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	66	3	69

Accuracy

100.0%

Counts

69 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (fma.f64 x x y) y)
▶	51.2%	#s(approx (+ (+ (* x x) y) y) (+.f64 y y))
▶	51.3%	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Compiler

Compiled 28 to 18 computations (35.7% saved)

series3.0ms (0.1%)

Memory

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

Counts

6 → 8

Calls

Call 1

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

Outputs
(* 2 y)
(+ (* 2 y) (pow x 2))
(pow x 2)
x
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
y
(* y (+ 2 (/ (pow x 2) y)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))

Calls

6 calls:

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

simplify145.0ms (5.8%)

Memory

11.6MiB live, 200.1MiB allocated; 44ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	36
1	57	36
2	187	36
3	924	36
4	4957	36
0	8133	32

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 6

Calls

Call 1

Inputs
(* 2 y)
(+ (* 2 y) (pow x 2))
(pow x 2)
x
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
y
(* y (+ 2 (/ (pow x 2) y)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))

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

rewrite52.0ms (2.1%)

Memory

-17.5MiB live, 57.8MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
0	11	30
1	50	30
0	415	28

Stop Event

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

Counts

6 → 26

Calls

Call 1

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

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 (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 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(neg.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
x
#s(approx (+ (+ (* x x) y) y) (*.f64 #s(literal 2 binary64) y))
(*.f64 #s(literal 2 binary64) y)
(*.f64 y #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y y #s(literal 0 binary64)))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y #s(literal 0 binary64))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y #s(literal 0 binary64))))
(+.f64 y y)
y

eval3.0ms (0.1%)

Memory: 6.3MiB live, 6.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 404 to 75 computations (81.4% saved)

prune2.0ms (0.1%)

Memory

6.6MiB live, 6.6MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	30	3	33

Accuracy

100.0%

Counts

33 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (fma.f64 x x y) y)
✓	51.2%	#s(approx (+ (+ (* x x) y) y) (+.f64 y y))
✓	51.3%	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Compiler

Compiled 74 to 34 computations (54.1% saved)

regimes71.0ms (2.8%)

Memory

-21.6MiB live, 23.1MiB allocated; 9ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

65.0ms	y
2.0ms	x
2.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
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)

regimes6.0ms (0.2%)

Memory

16.0MiB live, 16.0MiB allocated; 0ms collecting garbage

Counts

3 → 2

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
89.8%	2	`(*.f64 x x)`
78.2%	2	`(+.f64 (+.f64 (*.f64 x x) y) y)`
89.8%	2	`x`
70.3%	3	`y`

Compiler

Compiled 12 to 12 computations (0% saved)

regimes51.0ms (2%)

Memory

-30.9MiB live, 14.3MiB allocated; 6ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

47.0ms	y
1.0ms	x
1.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
51.2%	1	`y`
51.2%	1	`(+.f64 (+.f64 (*.f64 x x) y) y)`
51.2%	1	`(*.f64 x x)`
51.2%	1	`x`

Compiler

Compiled 12 to 12 computations (0% saved)

bsearch7.0ms (0.3%)

Memory

16.9MiB live, 16.9MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
6.0ms	1328152486.0624638	3801676012.908379

Samples

3.0ms

80×

valid

Compiler

Compiled 120 to 90 computations (25% saved)

Precisions

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

ival-add: 1.0ms (76% of total)

ival-mult: 1.0ms (76% of total)

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

adjust: 0.0ms (0% of total)

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

simplify53.0ms (2.1%)

Memory

2.7MiB live, 48.8MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	43
1	22	43
2	44	43
3	88	43
4	124	43
5	167	43
6	317	43
7	1503	43
8	5869	43

Stop Event

1×	node limit

Calls

Call 1

Inputs
(+.f64 (fma.f64 x x y) y)
(if (<=.f64 x #s(literal 1650000000 binary64)) #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #s(approx (+ (+ (* x x) y) y) (*.f64 x x)))
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))

Outputs
(+.f64 (fma.f64 x x y) y)
(if (<=.f64 x #s(literal 1650000000 binary64)) #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #s(approx (+ (+ (* x x) y) y) (*.f64 x x)))
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))

derivations101.0ms (4%)

Memory

-1.5MiB live, 98.3MiB allocated; 11ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 43 to 14 computations (67.4% saved)

preprocess22.0ms (0.9%)

Memory: 17.2MiB live, 62.9MiB allocated; 3ms collecting garbage
Remove: (abs x)
Compiler: Compiled 126 to 56 computations (55.6% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample1.2s (46.7%)

explain88.0ms (3.5%)

preprocess233.0ms (9.3%)

eval0.0ms (0%)

prune0.0ms (0%)

series4.0ms (0.2%)

simplify227.0ms (9%)

rewrite41.0ms (1.6%)

eval12.0ms (0.5%)

prune2.0ms (0.1%)

series3.0ms (0.1%)

simplify162.0ms (6.4%)

rewrite40.0ms (1.6%)

eval6.0ms (0.2%)

prune6.0ms (0.2%)

series3.0ms (0.1%)

simplify145.0ms (5.8%)

rewrite52.0ms (2.1%)

eval3.0ms (0.1%)

prune2.0ms (0.1%)

regimes71.0ms (2.8%)

regimes6.0ms (0.2%)

regimes51.0ms (2%)

bsearch7.0ms (0.3%)

simplify53.0ms (2.1%)

derivations101.0ms (4%)

preprocess22.0ms (0.9%)

end0.0ms (0%)

Profiling