Metrics for Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze21.0ms (0.8%)

Memory

-27.5MiB live, 12.0MiB 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
75%	74.9%	25%	0.1%	0%	0%	0%	5
75%	74.9%	25%	0.1%	0%	0%	0%	6
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	7
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	8
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	9
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	10
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	11
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample663.0ms (23.8%)

Memory

8.9MiB live, 326.3MiB allocated

Samples

409.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 183.0ms

ival-div: 94.0ms (51.5% of total)

ival-add: 80.0ms (43.8% of total)

ival-true: 6.0ms (3.3% of total)

ival-assert: 3.0ms (1.6% of total)

Bogosity

explain72.0ms (2.6%)

Memory

-15.1MiB live, 29.6MiB allocated

FPErrors

Click to see full error table

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

46.0ms

512×

valid

Compiler

Compiled 56 to 24 computations (57.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-add: 5.0ms (57% of total)

ival-div: 3.0ms (34.2% of total)

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

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

preprocess105.0ms (3.8%)

Memory

7.3MiB live, 7.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	42	35
2	106	35
3	315	35
4	1263	35
5	2381	35
6	3245	35
7	4081	35
8	4614	35
9	4736	35
10	4768	35
11	4844	35
12	4982	35
0	5	7
0	8	7
1	11	7
2	14	7
3	16	7
0	16	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify3.0ms (0.1%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	-384	(/.f64 (+.f64 x y) (+.f64 y y))
cost-diff	-128	(+.f64 y y)
cost-diff	0	(+.f64 x y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	11	15
2	14	15
3	16	15
0	16	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize15.0ms (0.5%)

Memory

10.3MiB live, 10.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 y y)
accuracy	0.0	(+.f64 x y)
accuracy	0.0078125	(/.f64 (+.f64 x y) (+.f64 y y))

Samples

10.0ms

256×

valid

Compiler

Compiled 32 to 12 computations (62.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-div: 2.0ms (47% of total)

ival-add: 2.0ms (47% of total)

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

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

series5.0ms (0.2%)

Memory

5.5MiB live, 5.5MiB allocated

Counts

3 → 13

Calls

Call 1

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

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

Calls

6 calls:

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

simplify99.0ms (3.6%)

Memory

5.3MiB live, 44.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	47
1	95	47
2	195	47
3	545	47
4	2439	47
5	5417	47
6	6656	47
7	7612	47
0	8037	44

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 11

Calls

Call 1

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

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

rewrite74.0ms (2.7%)

Memory

2.2MiB live, 40.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	38	13
0	305	13

Stop Event

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

Counts

3 → 61

Calls

Call 1

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

Outputs
(.f64 (.f64 (+.f64 y x) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (-.f64 x y)))
(.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 y (-.f64 y x) (.f64 x x))))
(/.f64 (-.f64 (.f64 y y) (.f64 x x)) (-.f64 y x))
(/.f64 (neg.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (neg.f64 (-.f64 x y)))
(/.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 y (-.f64 y x) (*.f64 x x))))
(/.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (-.f64 x y))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (*.f64 (+.f64 y x) (-.f64 x y))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y (-.f64 y x) (*.f64 x x)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 y y (-.f64 (.f64 x x) (.f64 y x))))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 y (-.f64 y x) (*.f64 x x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (.f64 y y) (-.f64 x y)))
(+.f64 y x)
(+.f64 x y)
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y y #s(literal 0 binary64)))
(*.f64 #s(literal -2 binary64) y)
(.f64 #s(literal -1 binary64) (.f64 #s(literal -2 binary64) y))
(*.f64 #s(literal 2 binary64) (neg.f64 y))
(*.f64 #s(literal 2 binary64) y)
(.f64 #s(literal 1 binary64) (.f64 #s(literal -2 binary64) y))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(*.f64 y #s(literal 2 binary64))
(pow.f64 (*.f64 #s(literal -2 binary64) y) #s(literal -1 binary64))
(/.f64 #s(literal 1/2 binary64) y)
(/.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 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) y))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) (neg.f64 (fma.f64 y y #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)))
(neg.f64 (*.f64 #s(literal -2 binary64) y))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -2 binary64) y))
(+.f64 (neg.f64 y) (neg.f64 y))
(+.f64 y y)
(*.f64 (/.f64 (+.f64 y x) #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 (+.f64 y x) (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y y #s(literal 0 binary64)))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 (+.f64 y x) #s(literal 0 binary64)) #s(literal 0 binary64)))
(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y))
(.f64 (.f64 #s(literal -2 binary64) y) (+.f64 y x))
(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
(pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 y (+.f64 y x))) #s(literal -1 binary64))
(/.f64 (/.f64 (+.f64 y x) #s(literal 2 binary64)) y)
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (*.f64 #s(literal -2 binary64) y)) (-.f64 x y))
(/.f64 (.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (.f64 #s(literal -2 binary64) y)) (fma.f64 y (-.f64 y x) (*.f64 x x)))
(/.f64 (.f64 (+.f64 y x) #s(literal 1 binary64)) (.f64 #s(literal -2 binary64) y))
(/.f64 (neg.f64 (neg.f64 (+.f64 y x))) (*.f64 #s(literal -2 binary64) y))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) #s(literal 1 binary64)) (.f64 (-.f64 x y) (.f64 #s(literal -2 binary64) y)))
(/.f64 (.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 y (-.f64 y x) (.f64 x x)) (.f64 #s(literal -2 binary64) y)))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 #s(literal 2 binary64) (/.f64 y (+.f64 y x)))))
(/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (.f64 (*.f64 #s(literal -2 binary64) y) (-.f64 x y)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 y (+.f64 y x))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 y (+.f64 y x))))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (.f64 (.f64 #s(literal -2 binary64) y) (fma.f64 y (-.f64 y x) (*.f64 x x))))
(/.f64 (neg.f64 (+.f64 y x)) (*.f64 #s(literal -2 binary64) y))
(/.f64 (+.f64 y x) (*.f64 #s(literal -2 binary64) y))
(neg.f64 (*.f64 (/.f64 (+.f64 y x) #s(literal 0 binary64)) #s(literal 0 binary64)))

eval35.0ms (1.3%)

Memory: -17.6MiB live, 19.7MiB allocated
Compiler: Compiled 801 to 172 computations (78.5% saved)

prune4.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	61	5	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	6	67

Accuracy

100.0%

Counts

67 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (+.f64 x y) (+.f64 y y))
▶	1.1%	(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
▶	4.3%	(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y))
▶	99.9%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64)))
▶	51.9%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
▶	49.6%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Compiler

Compiled 109 to 81 computations (25.7% saved)

simplify116.0ms (4.2%)

Memory

-0.1MiB live, 42.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
cost-diff	0	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
cost-diff	0	(*.f64 #s(literal -2 binary64) y)
cost-diff	0	(+.f64 y x)
cost-diff	0	(neg.f64 (+.f64 y x))
cost-diff	128	(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y))
cost-diff	0	(*.f64 #s(literal -2 binary64) y)
cost-diff	0	(+.f64 y x)
cost-diff	0	(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
cost-diff	0	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64)))

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	18	97
0	26	97
1	48	97
2	107	96
3	313	96
4	543	96
5	733	96
6	1395	93
7	3161	93
8	3738	93
9	3836	93
10	3885	93
11	3918	93
12	3918	93
13	3918	93
0	3918	93

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize62.0ms (2.2%)

Memory

6.0MiB live, 83.9MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.1953125	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
accuracy	30.66661563586506	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
accuracy	0.0	(+.f64 y x)
accuracy	0.0	(*.f64 #s(literal -2 binary64) y)
accuracy	0.0	(neg.f64 (+.f64 y x))
accuracy	0.00390625	(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y))
accuracy	0.0	(+.f64 y x)
accuracy	0.0	(*.f64 #s(literal -2 binary64) y)
accuracy	0.00390625	(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
accuracy	32.248358868354735	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.0	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64)))
accuracy	0.0859375	(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))

Samples

49.0ms

256×

valid

Compiler

Compiled 182 to 35 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-div: 20.0ms (55.9% of total)

ival-add: 9.0ms (25.1% of total)

ival-mult: 6.0ms (16.8% of total)

ival-neg: 1.0ms (2.8% of total)

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

exact: 0.0ms (0% of total)

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

series14.0ms (0.5%)

Memory

-11.0MiB live, 26.5MiB allocated

Counts

11 → 37

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	((/ (+ x y) (+ y y)) (+ (* (/ 1/2 y) x) 1/2) (/ 1/2 y) (/ (+ x y) (+ y y)) (* (+ y x) (* -2 y)) (+ y x) (* -2 y) (* (neg (+ y x)) (* -2 y)) (neg (+ y x)) (/ (+ x y) (+ y y)) (* (/ 1/2 y) x))
2.0ms	y	@	-inf	((/ (+ x y) (+ y y)) (+ (* (/ 1/2 y) x) 1/2) (/ 1/2 y) (/ (+ x y) (+ y y)) (* (+ y x) (* -2 y)) (+ y x) (* -2 y) (* (neg (+ y x)) (* -2 y)) (neg (+ y x)) (/ (+ x y) (+ y y)) (* (/ 1/2 y) x))
2.0ms	y	@	0	((/ (+ x y) (+ y y)) (+ (* (/ 1/2 y) x) 1/2) (/ 1/2 y) (/ (+ x y) (+ y y)) (* (+ y x) (* -2 y)) (+ y x) (* -2 y) (* (neg (+ y x)) (* -2 y)) (neg (+ y x)) (/ (+ x y) (+ y y)) (* (/ 1/2 y) x))
2.0ms	y	@	inf	((/ (+ x y) (+ y y)) (+ (* (/ 1/2 y) x) 1/2) (/ 1/2 y) (/ (+ x y) (+ y y)) (* (+ y x) (* -2 y)) (+ y x) (* -2 y) (* (neg (+ y x)) (* -2 y)) (neg (+ y x)) (/ (+ x y) (+ y y)) (* (/ 1/2 y) x))
2.0ms	x	@	inf	((/ (+ x y) (+ y y)) (+ (* (/ 1/2 y) x) 1/2) (/ 1/2 y) (/ (+ x y) (+ y y)) (* (+ y x) (* -2 y)) (+ y x) (* -2 y) (* (neg (+ y x)) (* -2 y)) (neg (+ y x)) (/ (+ x y) (+ y y)) (* (/ 1/2 y) x))

simplify102.0ms (3.7%)

Memory

-12.1MiB live, 144.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	195
1	226	175
2	563	175
3	1637	175
4	4389	175
5	6619	175
0	8135	171

Stop Event

1×	iter limit
1×	node limit

Counts

37 → 35

Calls

Call 1

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

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

rewrite67.0ms (2.4%)

Memory

28.8MiB live, 74.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	75
0	26	74
1	107	74
0	782	74

Stop Event

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

Counts

11 → 287

Calls

Call 1

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

Outputs
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64)))
(.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 2 binary64) y) x #s(literal -1/2 binary64))))
(.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 2 binary64) y) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (neg.f64 (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal 3 binary64)))) (neg.f64 (-.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (*.f64 #s(literal 2 binary64) y) x) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) y) x #s(literal -1/2 binary64)) (-.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal 1/2 binary64))) (+.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) y) x) #s(literal 3 binary64)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal 2 binary64)) (.f64 (.f64 (*.f64 #s(literal 2 binary64) y) x) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal 3 binary64))) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (*.f64 #s(literal 2 binary64) y) x) #s(literal 1/2 binary64))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (pow.f64 y #s(literal -1 binary64)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 y #s(literal -1 binary64)) x) #s(literal 1/2 binary64))
(fma.f64 x (*.f64 #s(literal 2 binary64) y) #s(literal 1/2 binary64))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 2 binary64) y) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 #s(literal 2 binary64) y) x #s(literal -1/2 binary64))))
(+.f64 (.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 2 binary64) y) x))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y y #s(literal 0 binary64)))
(*.f64 #s(literal 2 binary64) (neg.f64 y))
(*.f64 #s(literal 2 binary64) y)
(.f64 #s(literal -1 binary64) (.f64 #s(literal 2 binary64) y))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(*.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) y))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 y)))
(*.f64 #s(literal -2 binary64) y)
(*.f64 #s(literal 1/2 binary64) (pow.f64 y #s(literal -1 binary64)))
(*.f64 y #s(literal 2 binary64))
(*.f64 y #s(literal -2 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) y) #s(literal -1 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 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 #s(literal 2 binary64) y))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) y))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) (neg.f64 (fma.f64 y y #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 (neg.f64 y) #s(literal -1/2 binary64))
(/.f64 #s(literal -1/2 binary64) (neg.f64 y))
(/.f64 #s(literal 1/2 binary64) (neg.f64 (neg.f64 y)))
(/.f64 #s(literal 1/2 binary64) y)
(/.f64 y #s(literal 1/2 binary64))
(neg.f64 (/.f64 #s(literal -1/2 binary64) y))
(neg.f64 (*.f64 #s(literal 2 binary64) y))
(fma.f64 #s(literal -1 binary64) y (neg.f64 y))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) y))
(+.f64 (neg.f64 y) (neg.f64 y))
(+.f64 y y)
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
(*.f64 (/.f64 (+.f64 y x) #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 (+.f64 y x) (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y y #s(literal 0 binary64)))
(.f64 (.f64 (neg.f64 (+.f64 y x)) y) #s(literal -2 binary64))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) y) #s(literal -1 binary64)) (+.f64 y x))
(.f64 (.f64 (+.f64 y x) y) #s(literal -2 binary64))
(.f64 (.f64 (neg.f64 (+.f64 y x)) #s(literal -2 binary64)) y)
(.f64 (.f64 #s(literal -2 binary64) (+.f64 y x)) (neg.f64 y))
(.f64 (.f64 #s(literal -2 binary64) (+.f64 y x)) y)
(.f64 #s(literal -1 binary64) (.f64 (/.f64 (+.f64 y x) #s(literal 0 binary64)) #s(literal 0 binary64)))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 (+.f64 y x) #s(literal 0 binary64)) #s(literal 0 binary64)))
(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal 2 binary64) y))
(.f64 (.f64 #s(literal 2 binary64) y) (neg.f64 (+.f64 y x)))
(.f64 (.f64 #s(literal 2 binary64) y) (+.f64 y x))
(.f64 #s(literal -2 binary64) (.f64 y (neg.f64 (+.f64 y x))))
(.f64 #s(literal -2 binary64) (.f64 y (+.f64 y x)))
(.f64 (+.f64 y x) (.f64 #s(literal 2 binary64) y))
(.f64 y (.f64 (neg.f64 (+.f64 y x)) #s(literal -2 binary64)))
(.f64 y (.f64 #s(literal -2 binary64) (+.f64 y x)))
(pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 y (+.f64 y x))) #s(literal -1 binary64))
(/.f64 (/.f64 (+.f64 y x) #s(literal 2 binary64)) y)
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 y x)) (*.f64 #s(literal 2 binary64) y)) (-.f64 y x))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (*.f64 #s(literal 2 binary64) y)) (-.f64 x y))
(/.f64 (.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (.f64 #s(literal 2 binary64) y)) (fma.f64 x (-.f64 x y) (*.f64 y y)))
(/.f64 (.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (.f64 #s(literal 2 binary64) y)) (fma.f64 y (-.f64 y x) (*.f64 x x)))
(/.f64 (.f64 (+.f64 y x) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) y))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) y) (*.f64 (+.f64 y x) (-.f64 y x))) (-.f64 y x))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) y) (*.f64 (+.f64 y x) (-.f64 x y))) (-.f64 x y))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) y) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x y) (*.f64 y y)))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) y) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 y (-.f64 y x) (*.f64 x x)))
(/.f64 (neg.f64 (neg.f64 (+.f64 y x))) (*.f64 #s(literal 2 binary64) y))
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(*.f64 #s(literal 1/2 binary64) (/.f64 x y))
(.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 y #s(literal -1 binary64)) x))
(.f64 x (.f64 #s(literal 2 binary64) y))
(/.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 2 binary64) y))
(/.f64 (*.f64 #s(literal -1/2 binary64) x) (neg.f64 y))
(/.f64 (.f64 x #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) y))
(/.f64 (*.f64 x #s(literal -1/2 binary64)) (neg.f64 y))
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) x)) (neg.f64 y))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
(/.f64 #s(literal 1 binary64) (/.f64 y (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 x (*.f64 #s(literal 2 binary64) y))

eval32.0ms (1.2%)

Memory: 6.4MiB live, 83.1MiB allocated
Compiler: Compiled 4 045 to 642 computations (84.1% saved)

prune9.0ms (0.3%)

Memory

-10.1MiB live, 28.2MiB allocated

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	255	5	260
Fresh	0	0	0
Picked	3	2	5
Done	1	0	1
Total	259	7	266

Accuracy

100.0%

Counts

266 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64)))
▶	26.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
▶	52.1%	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
▶	3.7%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
✓	49.6%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
▶	1.9%	#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 #s(literal -2 binary64) y) y))
▶	3.4%	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 #s(literal 2 binary64) y) y))

Compiler

Compiled 157 to 110 computations (29.9% saved)

simplify141.0ms (5.1%)

Memory

-11.0MiB live, 71.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal -2 binary64) y)
cost-diff	0	(.f64 (.f64 #s(literal -2 binary64) y) y)
cost-diff	0	#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 #s(literal -2 binary64) y) y))
cost-diff	0	(*.f64 #s(literal 2 binary64) y)
cost-diff	0	(.f64 (.f64 #s(literal 2 binary64) y) y)
cost-diff	0	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 #s(literal 2 binary64) y) y))
cost-diff	-128	(+.f64 y y)
cost-diff	0	(fma.f64 (+.f64 y y) x #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
cost-diff	-128	(+.f64 y y)
cost-diff	0	(*.f64 (+.f64 y y) x)
cost-diff	0	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
cost-diff	0	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	120
0	36	120
1	65	120
2	135	119
3	347	119
4	549	119
5	765	119
6	1479	119
7	3118	119
8	3613	119
9	3751	119
10	3809	119
11	3821	119
12	3823	119
13	3823	119
14	3863	119
15	3891	119
16	3891	119
0	3891	116

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize57.0ms (2.1%)

Memory

18.7MiB live, 138.6MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.0	(.f64 (.f64 #s(literal -2 binary64) y) y)
accuracy	0.0	(*.f64 #s(literal -2 binary64) y)
accuracy	28.69412908951727	#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 #s(literal -2 binary64) y) y))
accuracy	0.0	(.f64 (.f64 #s(literal 2 binary64) y) y)
accuracy	0.0	(*.f64 #s(literal 2 binary64) y)
accuracy	28.69412908951727	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 #s(literal 2 binary64) y) y))
accuracy	0.0	(fma.f64 (+.f64 y y) x #s(literal 1/2 binary64))
accuracy	0.0	(+.f64 y y)
accuracy	47.33969544468541	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
accuracy	0.0	(+.f64 y y)
accuracy	0.0	(*.f64 (+.f64 y y) x)
accuracy	61.60913335851638	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
accuracy	0.0	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	30.66661563586506	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))

Samples

44.0ms

256×

valid

Compiler

Compiled 212 to 50 computations (76.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 11.0ms (50.2% of total)

ival-add: 5.0ms (22.8% of total)

ival-div: 4.0ms (18.3% of total)

ival-neg: 1.0ms (4.6% of total)

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

exact: 0.0ms (0% of total)

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

series13.0ms (0.5%)

Memory

-6.4MiB live, 32.6MiB allocated

Counts

14 → 27

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	((/ (+ x y) (+ y y)) (/ (* 1/2 x) y) (* 1/2 x) (/ (+ x y) (+ y y)) (* (+ y y) x) (+ y y) (/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2) (* (neg (+ y x)) (* -2 y)) (* (* 2 y) y) (* 2 y) (* (+ y x) (* -2 y)) (* (* -2 y) y) (* -2 y))
2.0ms	y	@	-inf	((/ (+ x y) (+ y y)) (/ (* 1/2 x) y) (* 1/2 x) (/ (+ x y) (+ y y)) (* (+ y y) x) (+ y y) (/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2) (* (neg (+ y x)) (* -2 y)) (* (* 2 y) y) (* 2 y) (* (+ y x) (* -2 y)) (* (* -2 y) y) (* -2 y))
2.0ms	y	@	inf	((/ (+ x y) (+ y y)) (/ (* 1/2 x) y) (* 1/2 x) (/ (+ x y) (+ y y)) (* (+ y y) x) (+ y y) (/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2) (* (neg (+ y x)) (* -2 y)) (* (* 2 y) y) (* 2 y) (* (+ y x) (* -2 y)) (* (* -2 y) y) (* -2 y))
2.0ms	y	@	0	((/ (+ x y) (+ y y)) (/ (* 1/2 x) y) (* 1/2 x) (/ (+ x y) (+ y y)) (* (+ y y) x) (+ y y) (/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2) (* (neg (+ y x)) (* -2 y)) (* (* 2 y) y) (* 2 y) (* (+ y x) (* -2 y)) (* (* -2 y) y) (* -2 y))
2.0ms	x	@	-inf	((/ (+ x y) (+ y y)) (/ (* 1/2 x) y) (* 1/2 x) (/ (+ x y) (+ y y)) (* (+ y y) x) (+ y y) (/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2) (* (neg (+ y x)) (* -2 y)) (* (* 2 y) y) (* 2 y) (* (+ y x) (* -2 y)) (* (* -2 y) y) (* -2 y))

simplify100.0ms (3.6%)

Memory

-20.3MiB live, 137.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	181
1	197	161
2	516	161
3	1180	161
4	2985	161
5	5697	161
6	7576	161
0	8022	153

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 27

Calls

Call 1

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

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

rewrite52.0ms (1.9%)

Memory

1.4MiB live, 80.3MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	105
0	36	102
1	122	96
0	800	96

Stop Event

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

Counts

14 → 298

Calls

Call 1

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

Outputs
#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 #s(literal 2 binary64) y) x))
(.f64 (.f64 x #s(literal 2 binary64)) y)
(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
(.f64 (pow.f64 y #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) x))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 #s(literal 2 binary64) y) x))
(.f64 (.f64 y x) #s(literal 2 binary64))
(.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) (neg.f64 y)))
(.f64 #s(literal 2 binary64) (.f64 y x))
(.f64 (.f64 #s(literal 2 binary64) y) x)
(.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 y #s(literal -1 binary64)))
(*.f64 #s(literal 1/2 binary64) (/.f64 x y))
(.f64 y (.f64 #s(literal 2 binary64) x))
(.f64 x (.f64 #s(literal 1/2 binary64) (pow.f64 y #s(literal -1 binary64))))
(.f64 x (.f64 #s(literal 2 binary64) y))
(pow.f64 (/.f64 y (*.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) x) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) y)
(/.f64 (*.f64 x #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (.f64 x (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) x)) (neg.f64 (neg.f64 y)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 y (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 y (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 y (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (*.f64 #s(literal -1/2 binary64) x) (neg.f64 y))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
(neg.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) x) y))
(neg.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (neg.f64 y)))
(fma.f64 y x (*.f64 y x))
(fma.f64 x y (*.f64 y x))
(+.f64 (.f64 y x) (.f64 y x))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 #s(literal 2 binary64) y) x))
(.f64 (.f64 x #s(literal 2 binary64)) y)
(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
(.f64 (pow.f64 y #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) x))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 #s(literal 2 binary64) y) x))
(.f64 (.f64 y x) #s(literal 2 binary64))
(.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) (neg.f64 y)))
(.f64 #s(literal 2 binary64) (.f64 y x))
(.f64 (.f64 #s(literal 2 binary64) y) x)
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(pow.f64 (*.f64 #s(literal 2 binary64) y) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 0 binary64) y) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) y) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (.f64 y (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y y #s(literal 0 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 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 #s(literal 2 binary64) y))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) y))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) (neg.f64 (fma.f64 y y #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 #s(literal 1/2 binary64) y)
(neg.f64 (*.f64 #s(literal 2 binary64) y))
(fma.f64 #s(literal -1 binary64) y (neg.f64 y))
(fma.f64 y y (*.f64 y y))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) y))
(+.f64 (.f64 y y) (.f64 y y))
(+.f64 (neg.f64 y) (neg.f64 y))
(+.f64 y y)

eval28.0ms (1%)

Memory: 22.5MiB live, 67.1MiB allocated
Compiler: Compiled 2 665 to 432 computations (83.8% saved)

prune6.0ms (0.2%)

Memory

-18.6MiB live, 20.2MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	0	0	0
Picked	0	5	5
Done	0	2	2
Total	156	8	164

Accuracy

100.0%

Counts

164 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64)))
✓	26.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
✓	52.1%	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
✓	3.7%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
✓	49.6%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
✓	1.9%	#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 #s(literal -2 binary64) y) y))
▶	3.1%	#s(approx (* (+ y x) (* -2 y)) (*.f64 #s(literal 2 binary64) y))
✓	3.4%	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 #s(literal 2 binary64) y) y))

Compiler

Compiled 101 to 72 computations (28.7% saved)

simplify4.0ms (0.2%)

Memory

8.2MiB live, 8.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 #s(literal 2 binary64) y)
cost-diff	0	#s(approx (* (+ y x) (* -2 y)) (*.f64 #s(literal 2 binary64) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
0	10	16
1	16	16
2	31	16
3	54	16
4	66	16
0	66	16

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize18.0ms (0.6%)

Memory

0.5MiB live, 39.4MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(*.f64 #s(literal 2 binary64) y)
accuracy	61.43311704918775	#s(approx (* (+ y x) (* -2 y)) (*.f64 #s(literal 2 binary64) y))

Samples

12.0ms

256×

valid

Compiler

Compiled 30 to 19 computations (36.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-mult: 5.0ms (73.8% of total)

ival-add: 1.0ms (14.8% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB allocated

Counts

2 → 8

Calls

Call 1

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

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

Calls

6 calls:

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

simplify91.0ms (3.3%)

Memory

-23.8MiB live, 134.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	58
1	81	48
2	200	48
3	459	48
4	1085	48
5	2695	48
6	6247	48
0	8181	48

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 8

Calls

Call 1

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

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

rewrite188.0ms (6.8%)

Memory

14.6MiB live, 290.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
0	10	14
1	29	14
2	165	14
3	1562	14
0	9271	14

Stop Event

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

Counts

2 → 3

Calls

Call 1

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

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

eval1.0ms (0%)

Memory: 2.0MiB live, 2.0MiB allocated
Compiler: Compiled 89 to 26 computations (70.8% saved)

prune4.0ms (0.1%)

Memory

10.2MiB live, 10.2MiB allocated

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	7	0	7
Fresh	0	0	0
Picked	0	1	1
Done	0	7	7
Total	7	8	15

Accuracy

100.0%

Counts

15 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64)))
✓	26.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
✓	52.1%	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
✓	3.7%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
✓	49.6%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
✓	1.9%	#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 #s(literal -2 binary64) y) y))
✓	3.1%	#s(approx (* (+ y x) (* -2 y)) (*.f64 #s(literal 2 binary64) y))
✓	3.4%	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 #s(literal 2 binary64) y) y))

Compiler

Compiled 237 to 113 computations (52.3% saved)

regimes14.0ms (0.5%)

Memory

-10.5MiB live, 28.2MiB allocated

Counts

12 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	y
4.0ms	x
3.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

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

Compiler

Compiled 9 to 9 computations (0% saved)

regimes11.0ms (0.4%)

Memory

26.9MiB live, 26.9MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	y
4.0ms	x
3.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 9 to 9 computations (0% saved)

regimes13.0ms (0.5%)

Memory

-14.4MiB live, 24.5MiB allocated

Counts

10 → 3

Calls

Call 1

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

Outputs

#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))

#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))

Calls

3 calls:

5.0ms	(/.f64 (+.f64 x y) (+.f64 y y))
3.0ms	x
3.0ms	y

Results

Accuracy	Segments	Branch
79.0%	3	`x`
73.7%	3	`y`
98.4%	3	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 9 to 9 computations (0% saved)

regimes3.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB allocated

Counts

9 → 3

Calls

Call 1

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

Outputs

#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))

#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))

Calls

1 calls:

3.0ms

(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
98.3%	3	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 7 to 5 computations (28.6% saved)

regimes18.0ms (0.6%)

Memory

-14.5MiB live, 31.5MiB allocated

Accuracy

Total -31.1b remaining (-96.4%)

Threshold costs -31.1b (-96.4%)

Counts

8 → 1

Calls

Call 1

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

Outputs
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Calls

3 calls:

12.0ms	x
3.0ms	y
2.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
49.6%	1	`y`
49.6%	1	`x`
49.6%	1	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 9 to 9 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.506607556047701	25219.266990051565
0.0ms	-440305800.42894334	0.4770093915191236

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.506607556047701	25219.266990051565
0.0ms	-440305800.42894334	0.4770093915191236

Compiler

Compiled 10 to 10 computations (0% saved)

simplify12.0ms (0.4%)

Memory

-21.3MiB live, 17.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	116
1	35	116
2	38	116
3	40	116

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (+.f64 x y) (+.f64 y y))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64)))
(if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -400000000 binary64)) #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y)) (if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal 1 binary64)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y))))
(if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -400000000 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) (if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal 1 binary64)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x))))
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Outputs
(/.f64 (+.f64 x y) (+.f64 y y))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64)))
(if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -400000000 binary64)) #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y)) (if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal 1 binary64)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y))))
(if (or (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -400000000 binary64)) (not (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal 1 binary64)))) #s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)))
(if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -400000000 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) (if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal 1 binary64)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x))))
(if (or (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -400000000 binary64)) (not (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal 1 binary64)))) #s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)))
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

soundness462.0ms (16.6%)

Memory

27.1MiB live, 222.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	75
0	26	74
1	107	74
0	782	74
0	34	47
1	95	47
2	195	47
3	545	47
4	2439	47
5	5417	47
6	6656	47
7	7612	47
0	8037	44

Stop Event

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

Compiler

Compiled 148 to 59 computations (60.1% saved)

preprocess41.0ms (1.5%)

Memory: 9.3MiB live, 90.9MiB allocated
Compiler: Compiled 260 to 74 computations (71.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze21.0ms (0.8%)

sample663.0ms (23.8%)

explain72.0ms (2.6%)

preprocess105.0ms (3.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize15.0ms (0.5%)

series5.0ms (0.2%)

simplify99.0ms (3.6%)

rewrite74.0ms (2.7%)

eval35.0ms (1.3%)

prune4.0ms (0.1%)

simplify116.0ms (4.2%)

localize62.0ms (2.2%)

series14.0ms (0.5%)

simplify102.0ms (3.7%)

rewrite67.0ms (2.4%)

eval32.0ms (1.2%)

prune9.0ms (0.3%)

simplify141.0ms (5.1%)

localize57.0ms (2.1%)

series13.0ms (0.5%)

simplify100.0ms (3.6%)

rewrite52.0ms (1.9%)

eval28.0ms (1%)

prune6.0ms (0.2%)

simplify4.0ms (0.2%)

localize18.0ms (0.6%)

series2.0ms (0.1%)

simplify91.0ms (3.3%)

rewrite188.0ms (6.8%)

eval1.0ms (0%)

prune4.0ms (0.1%)

regimes14.0ms (0.5%)

regimes11.0ms (0.4%)

regimes13.0ms (0.5%)

regimes3.0ms (0.1%)

regimes18.0ms (0.6%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

simplify12.0ms (0.4%)

soundness462.0ms (16.6%)

preprocess41.0ms (1.5%)

end0.0ms (0%)

Profiling