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

start0.0ms (0%)

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

analyze81.0ms (3.5%)

Memory

-22.7MiB live, 21.6MiB allocated; 18ms collecting garbage

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)

sample791.0ms (33.9%)

Memory

38.4MiB live, 1 404.9MiB allocated; 235ms collecting garbage

Samples

525.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 262.0ms

ival-add: 170.0ms (64.9% of total)

ival-div: 81.0ms (30.9% of total)

ival-true: 6.0ms (2.3% of total)

ival-assert: 3.0ms (1.1% of total)

adjust: 2.0ms (0.8% of total)

Bogosity

explain79.0ms (3.4%)

Memory

-19.7MiB live, 148.1MiB allocated; 15ms collecting garbage

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

50.0ms

512×

valid

Compiler

Compiled 41 to 19 computations (53.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-add: 28.0ms (85.9% of total)

ival-div: 4.0ms (12.3% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess19.0ms (0.8%)

Memory

3.0MiB live, 49.2MiB allocated; 3ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	39	39
2	108	39
3	246	35
4	396	35
5	456	35
6	469	35
0	5	7
0	8	7
1	14	7
2	24	7
3	36	7
4	42	7
0	42	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: 0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated; 0ms collecting garbage

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)

simplify4.0ms (0.2%)

Memory

11.2MiB live, 11.2MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	14	15
2	24	15
3	36	15
4	42	15
0	42	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)

localize16.0ms (0.7%)

Memory

-3.5MiB live, 43.4MiB allocated; 1ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 y y)
accuracy	0.0	(+.f64 x y)
accuracy	0.01171875	(/.f64 (+.f64 x y) (+.f64 y y))

Samples

10.0ms

256×

valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

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

ival-div: 2.0ms (45.3% of total)

ival-add: 2.0ms (45.3% of total)

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

adjust: 0.0ms (0% of total)

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

series7.0ms (0.3%)

Memory

-39.7MiB live, 12.0MiB allocated; 4ms collecting garbage

Counts

3 → 13

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	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))

simplify145.0ms (6.2%)

Memory

41.3MiB live, 178.8MiB allocated; 10ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	47
1	105	47
2	228	47
3	648	47
4	2049	47
5	4498	47
6	7409	47
0	8200	44

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 11

Calls

Call 1

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

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

rewrite83.0ms (3.6%)

Memory

2.7MiB live, 97.5MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	36	13
0	267	13

Stop Event

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

Counts

3 → 42

Calls

Call 1

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

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

eval10.0ms (0.4%)

Memory: -24.9MiB live, 19.1MiB allocated; 6ms collecting garbage
Compiler: Compiled 661 to 140 computations (78.8% saved)

prune2.0ms (0.1%)

Memory

7.2MiB live, 7.2MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	4	48

Accuracy

100.0%

Counts

48 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (+.f64 x y) (+.f64 y y))
▶	99.8%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64)))
▶	49.4%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 x y) #s(literal 1/2 binary64)))
▶	52.8%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Compiler

Compiled 43 to 30 computations (30.2% saved)

simplify20.0ms (0.9%)

Memory

-0.5MiB live, 41.6MiB allocated; 7ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	60
0	18	60
1	31	60
2	48	60
3	82	60
4	123	60
5	158	60
6	199	60
7	288	60
8	389	60
9	471	60
10	546	60
11	605	60
12	625	60
13	627	60
0	627	60

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize47.0ms (2%)

Memory

-10.4MiB live, 50.7MiB allocated; 8ms collecting garbage

Localize:

Found 7 expressions of interest:

New	Metric	Score
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	0.1015625	(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
accuracy	0.0	(/.f64 x y)
accuracy	0.0	(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
accuracy	32.360267816714014	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 x y) #s(literal 1/2 binary64)))
accuracy	30.19336638298339	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Samples

40.0ms

256×

valid

Compiler

Compiled 48 to 13 computations (72.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-div: 24.0ms (76.6% of total)

ival-add: 4.0ms (12.8% of total)

ival-mult: 3.0ms (9.6% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series8.0ms (0.3%)

Memory

8.8MiB live, 8.8MiB allocated; 0ms collecting garbage

Counts

7 → 8

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	y	@	inf	((/ (+ x y) (+ y y)) (/ (+ x y) (+ y y)) (* (/ x y) 1/2) (/ x y) (/ (+ x y) (+ y y)) (+ (* (/ 1/2 y) x) 1/2) (/ 1/2 y))
1.0ms	x	@	-inf	((/ (+ x y) (+ y y)) (/ (+ x y) (+ y y)) (* (/ x y) 1/2) (/ x y) (/ (+ x y) (+ y y)) (+ (* (/ 1/2 y) x) 1/2) (/ 1/2 y))
1.0ms	x	@	inf	((/ (+ x y) (+ y y)) (/ (+ x y) (+ y y)) (* (/ x y) 1/2) (/ x y) (/ (+ x y) (+ y y)) (+ (* (/ 1/2 y) x) 1/2) (/ 1/2 y))
1.0ms	y	@	-inf	((/ (+ x y) (+ y y)) (/ (+ x y) (+ y y)) (* (/ x y) 1/2) (/ x y) (/ (+ x y) (+ y y)) (+ (* (/ 1/2 y) x) 1/2) (/ 1/2 y))
1.0ms	y	@	0	((/ (+ x y) (+ y y)) (/ (+ x y) (+ y y)) (* (/ x y) 1/2) (/ x y) (/ (+ x y) (+ y y)) (+ (* (/ 1/2 y) x) 1/2) (/ 1/2 y))

simplify38.0ms (1.6%)

Memory

24.8MiB live, 24.8MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	60	40
2	135	40
3	316	40
4	486	40
5	725	40
6	1496	40
7	2189	40
8	2559	40
9	2559	40
0	2559	36

Stop Event

1×	iter limit
1×	saturated

Counts

8 → 8

Calls

Call 1

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

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

rewrite71.0ms (3%)

Memory

-16.3MiB live, 69.9MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	53
0	18	53
1	73	53
0	448	53

Stop Event

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

Counts

7 → 38

Calls

Call 1

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

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

eval4.0ms (0.2%)

Memory: 15.1MiB live, 15.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 787 to 139 computations (82.3% saved)

prune3.0ms (0.1%)

Memory

9.9MiB live, 9.9MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	41	2	43
Fresh	0	0	0
Picked	1	2	3
Done	1	0	1
Total	43	4	47

Accuracy

100.0%

Counts

47 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	49.4%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 x y) #s(literal 1/2 binary64)))
▶	49.3%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
✓	52.8%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Compiler

Compiled 49 to 34 computations (30.6% saved)

simplify28.0ms (1.2%)

Memory

-49.1MiB live, 55.0MiB allocated; 19ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	50
0	17	50
1	33	50
2	54	50
3	83	50
4	125	50
5	162	50
6	202	50
7	289	50
8	393	50
9	475	50
10	549	50
11	608	50
12	628	50
13	630	50
0	630	50

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

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

localize30.0ms (1.3%)

Memory

28.5MiB live, 73.0MiB allocated; 3ms collecting garbage

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 x y)
accuracy	0.0	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
accuracy	0.00390625	(fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.19921875	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
accuracy	32.360267816714014	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))

Samples

21.0ms

256×

valid

Compiler

Compiled 40 to 13 computations (67.5% saved)

Precisions

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

ival-div: 5.0ms (40.9% of total)

ival-add: 4.0ms (32.7% of total)

ival-mult: 3.0ms (24.5% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series5.0ms (0.2%)

Memory

13.1MiB live, 13.1MiB allocated; 0ms collecting garbage

Counts

6 → 8

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((/ (+ x y) (+ y y)) (* (/ 1/2 y) x) (/ 1/2 y) (/ (+ x y) (+ y y)) (+ (* (/ x y) 1/2) 1/2) (/ x y))
1.0ms	x	@	inf	((/ (+ x y) (+ y y)) (* (/ 1/2 y) x) (/ 1/2 y) (/ (+ x y) (+ y y)) (+ (* (/ x y) 1/2) 1/2) (/ x y))
1.0ms	y	@	-inf	((/ (+ x y) (+ y y)) (* (/ 1/2 y) x) (/ 1/2 y) (/ (+ x y) (+ y y)) (+ (* (/ x y) 1/2) 1/2) (/ x y))
1.0ms	y	@	inf	((/ (+ x y) (+ y y)) (* (/ 1/2 y) x) (/ 1/2 y) (/ (+ x y) (+ y y)) (+ (* (/ x y) 1/2) 1/2) (/ x y))
1.0ms	y	@	0	((/ (+ x y) (+ y y)) (* (/ 1/2 y) x) (/ 1/2 y) (/ (+ x y) (+ y y)) (+ (* (/ x y) 1/2) 1/2) (/ x y))

simplify35.0ms (1.5%)

Memory

-27.5MiB live, 18.1MiB allocated; 4ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	60	40
2	135	40
3	316	40
4	486	40
5	725	40
6	1496	40
7	2189	40
8	2559	40
9	2559	40
0	2559	36

Stop Event

1×	iter limit
1×	saturated

Counts

8 → 8

Calls

Call 1

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

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

rewrite46.0ms (2%)

Memory

17.8MiB live, 62.5MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	44
0	17	44
1	75	44
0	460	44

Stop Event

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

Counts

6 → 39

Calls

Call 1

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

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

eval5.0ms (0.2%)

Memory: 16.1MiB live, 16.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 790 to 146 computations (81.5% saved)

prune13.0ms (0.6%)

Memory

-23.6MiB live, 29.0MiB allocated; 9ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	44	4	48

Accuracy

100.0%

Counts

48 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	49.4%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 x y) #s(literal 1/2 binary64)))
✓	49.3%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
✓	52.8%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Compiler

Compiled 119 to 54 computations (54.6% saved)

regimes7.0ms (0.3%)

Memory

22.6MiB live, 22.6MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 9 computations (0% saved)

regimes8.0ms (0.4%)

Memory

-28.5MiB live, 16.6MiB allocated; 3ms collecting garbage

Counts

4 → 1

Calls

Call 1

Inputs
#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)) (*.f64 (/.f64 x y) #s(literal 1/2 binary64)))
#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:

5.0ms	y
2.0ms	x
1.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
99.8%	1	`(/.f64 (+.f64 x y) (+.f64 y y))`
99.8%	1	`x`
99.8%	1	`y`

Compiler

Compiled 9 to 9 computations (0% saved)

regimes5.0ms (0.2%)

Memory

19.5MiB live, 19.5MiB allocated; 0ms collecting garbage

Counts

3 → 3

Calls

Call 1

Inputs

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

Outputs

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.7%	3	`(/.f64 (+.f64 x y) (+.f64 y y))`
77.7%	3	`x`
74.4%	3	`y`

Compiler

Compiled 9 to 9 computations (0% saved)

regimes1.0ms (0.1%)

Memory

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

Counts

2 → 3

Calls

Call 1

Inputs
#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))

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:

1.0ms

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

Results

Accuracy	Segments	Branch
98.5%	3	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 7 to 5 computations (28.6% saved)

regimes25.0ms (1.1%)

Memory

-40.2MiB live, 7.1MiB allocated; 2ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

22.0ms	y
1.0ms	x
1.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
52.8%	1	`y`
52.8%	1	`x`
52.8%	1	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 9 to 9 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.5000014314376529	457.7401092533348
0.0ms	-76.02961079085563	0.49999999999896727

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch1.0ms (0%)

Memory

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

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.5000014314376529	457.7401092533348
0.0ms	-76.02961079085563	0.49999999999896727

Compiler

Compiled 10 to 10 computations (0% saved)

simplify78.0ms (3.3%)

Memory

12.4MiB live, 58.6MiB allocated; 4ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	123
1	40	123
2	49	123
3	64	123
4	92	123
5	150	123
6	335	123
7	1006	123
8	2503	123
9	3951	123
10	5868	123
11	7525	123

Stop Event

1×	node limit

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
#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 -50 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 x y) #s(literal 1/2 binary64))) (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 x y) #s(literal 1/2 binary64)))))
(if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -50 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
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
#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 -50 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 x y) #s(literal 1/2 binary64))) (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 x y) #s(literal 1/2 binary64)))))
(if (or (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -50 binary64)) (not (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal 1 binary64)))) #s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 x y) #s(literal 1/2 binary64))) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)))
(if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -50 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 -50 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))

derivations582.0ms (25%)

Memory

-16.8MiB live, 228.4MiB allocated; 34ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	53
0	18	53
1	73	53
0	448	53
0	34	47
1	105	47
2	228	47
3	648	47
4	2049	47
5	4498	47
6	7409	47
0	8200	44
0	20	40
1	60	40
2	135	40
3	316	40
4	486	40
5	725	40
6	1496	40
7	2189	40
8	2559	40
9	2559	40
0	2559	36

Stop Event

1×	done
1×	iter limit
1×	saturated
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Compiler

Compiled 123 to 28 computations (77.2% saved)

preprocess32.0ms (1.4%)

Memory: 36.3MiB live, 36.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 274 to 78 computations (71.5% saved)

end0.0ms (0%)

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

Iter	Nodes	Cost
0	15	41
1	39	39
2	108	39
3	246	35
4	396	35
5	456	35
6	469	35
0	5	7
0	8	7
1	14	7
2	24	7
3	36	7
4	42	7
0	42	7

Iter	Nodes	Cost
0	13	60
0	18	60
1	31	60
2	48	60
3	82	60
4	123	60
5	158	60
6	199	60
7	288	60
8	389	60
9	471	60
10	546	60
11	605	60
12	625	60
13	627	60
0	627	60

Iter	Nodes	Cost
0	12	50
0	17	50
1	33	50
2	54	50
3	83	50
4	125	50
5	162	50
6	202	50
7	289	50
8	393	50
9	475	50
10	549	50
11	608	50
12	628	50
13	630	50
0	630	50

Iter	Nodes	Cost
0	15	41
1	39	39
2	108	39
3	246	35
4	396	35
5	456	35
6	469	35
0	5	7
0	8	7
1	14	7
2	24	7
3	36	7
4	42	7
0	42	7

Iter	Nodes	Cost
0	13	60
0	18	60
1	31	60
2	48	60
3	82	60
4	123	60
5	158	60
6	199	60
7	288	60
8	389	60
9	471	60
10	546	60
11	605	60
12	625	60
13	627	60
0	627	60

Iter	Nodes	Cost
0	12	50
0	17	50
1	33	50
2	54	50
3	83	50
4	125	50
5	162	50
6	202	50
7	289	50
8	393	50
9	475	50
10	549	50
11	608	50
12	628	50
13	630	50
0	630	50

start0.0ms (0%)

analyze81.0ms (3.5%)

sample791.0ms (33.9%)

explain79.0ms (3.4%)

preprocess19.0ms (0.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.2%)

localize16.0ms (0.7%)

series7.0ms (0.3%)

simplify145.0ms (6.2%)

rewrite83.0ms (3.6%)

eval10.0ms (0.4%)

prune2.0ms (0.1%)

simplify20.0ms (0.9%)

localize47.0ms (2%)

series8.0ms (0.3%)

simplify38.0ms (1.6%)

rewrite71.0ms (3%)

eval4.0ms (0.2%)

prune3.0ms (0.1%)

simplify28.0ms (1.2%)

localize30.0ms (1.3%)

series5.0ms (0.2%)

simplify35.0ms (1.5%)

rewrite46.0ms (2%)

eval5.0ms (0.2%)

prune13.0ms (0.6%)

regimes7.0ms (0.3%)

regimes8.0ms (0.4%)

regimes5.0ms (0.2%)

regimes1.0ms (0.1%)

regimes25.0ms (1.1%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

simplify78.0ms (3.3%)

derivations582.0ms (25%)

preprocess32.0ms (1.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	15	41
1	39	39
2	108	39
3	246	35
4	396	35
5	456	35
6	469	35
0	5	7
0	8	7
1	14	7
2	24	7
3	36	7
4	42	7
0	42	7

Iter	Nodes	Cost
0	13	60
0	18	60
1	31	60
2	48	60
3	82	60
4	123	60
5	158	60
6	199	60
7	288	60
8	389	60
9	471	60
10	546	60
11	605	60
12	625	60
13	627	60
0	627	60

Iter	Nodes	Cost
0	12	50
0	17	50
1	33	50
2	54	50
3	83	50
4	125	50
5	162	50
6	202	50
7	289	50
8	393	50
9	475	50
10	549	50
11	608	50
12	628	50
13	630	50
0	630	50