Metrics for System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample879.0ms (22.7%)

Memory

14.0MiB live, 702.9MiB allocated

Samples

625.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 167.0ms

ival-mult: 114.0ms (68.5% of total)

ival-sub: 39.0ms (23.4% of total)

ival-true: 6.0ms (3.6% of total)

exact: 5.0ms (3% of total)

ival-assert: 3.0ms (1.8% of total)

Bogosity

explain111.0ms (2.9%)

Memory

24.2MiB live, 70.6MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`y`
-	-	`(-.f64 (*.f64 x x) y)`
-	-	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
-	-	`#s(literal 1/2 binary64)`
-	-	`(*.f64 x x)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

74.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-mult: 58.0ms (94.5% of total)

ival-sub: 2.0ms (3.3% of total)

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

exact: 0.0ms (0% of total)

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

preprocess88.0ms (2.3%)

Memory

-58.0MiB live, 15.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	37
1	41	37
2	74	37
3	101	37
4	125	37
0	6	7
0	9	7
1	14	7
2	27	7
3	46	7
4	58	7
0	58	7

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0.1%)

Memory

3.7MiB live, 3.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	9	18
1	14	18
2	27	18
3	46	18
4	58	18
0	58	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize15.0ms (0.4%)

Memory

25.0MiB live, 25.0MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.0	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
accuracy	0.00390625	(-.f64 (*.f64 x x) y)

Samples

11.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-mult: 3.0ms (62.4% of total)

ival-sub: 1.0ms (20.8% of total)

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

exact: 0.0ms (0% of total)

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

series30.0ms (0.8%)

Memory

-39.4MiB live, 5.7MiB allocated

Counts

3 → 13

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
27.0ms	y	@	-inf	((* 1/2 (- (* x x) y)) (- (* x x) y) (* x x))
1.0ms	x	@	inf	((* 1/2 (- (* x x) y)) (- (* x x) y) (* x x))
1.0ms	x	@	0	((* 1/2 (- (* x x) y)) (- (* x x) y) (* x x))
1.0ms	y	@	0	((* 1/2 (- (* x x) y)) (- (* x x) y) (* x x))
0.0ms	x	@	-inf	((* 1/2 (- (* x x) y)) (- (* x x) y) (* x x))

simplify260.0ms (6.7%)

Memory

19.1MiB live, 201.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	74
1	109	66
2	362	66
3	1514	66
4	4452	66
5	6334	66
6	6943	66
7	7241	66
0	8542	66

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 13

Calls

Call 1

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

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

rewrite252.0ms (6.5%)

Memory

3.7MiB live, 151.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	9	15
1	29	15
2	197	15
3	2129	15
0	9773	13

Stop Event

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

Counts

3 → 239

Calls

Call 1

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

Outputs
(.f64 (/.f64 (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))))) (/.f64 (fma.f64 x x y) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(.f64 (/.f64 (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))) (/.f64 (fma.f64 x x y) (fma.f64 x x y)))
(*.f64 (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))))) (/.f64 #s(literal -1/2 binary64) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))))) (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))) (fma.f64 x x y))
(.f64 (/.f64 (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)) (fma.f64 x x y)) (/.f64 (fma.f64 x x y) (/.f64 (fma.f64 x x y) (fma.f64 x x y))))
(*.f64 (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))) (/.f64 #s(literal -1/2 binary64) (fma.f64 x x y)))
(.f64 (/.f64 (fma.f64 x x y) (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))))) (/.f64 (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(.f64 (/.f64 (fma.f64 x x y) (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))) (/.f64 (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)) (fma.f64 x x y)))
(*.f64 (/.f64 #s(literal -1/2 binary64) (fma.f64 x x y)) (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (/.f64 (fma.f64 x x y) (fma.f64 x x y))))
(.f64 (/.f64 (fma.f64 x x y) (fma.f64 x x y)) (/.f64 (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)) (/.f64 (fma.f64 x x y) (fma.f64 x x y))))
(.f64 (/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/2 binary64)) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (.f64 (fma.f64 x x y) y) #s(literal 3 binary64)))) (fma.f64 (.f64 (fma.f64 x x y) y) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x y)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))
(.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (fma.f64 x x y)) (fma.f64 x x y)) (fma.f64 x x y))
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 x x y)))
(*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (/.f64 #s(literal -1/2 binary64) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (fma.f64 x x y) (/.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x x y) (fma.f64 x x y))))
(*.f64 (fma.f64 x x y) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x x y))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/2 binary64)))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (fma.f64 x x y))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/2 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))
(/.f64 (neg.f64 (*.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (fma.f64 x x y))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))
(/.f64 (*.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 x x y))
(+.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64)) (fma.f64 x x y)) (/.f64 (.f64 (*.f64 (neg.f64 y) y) #s(literal 1/2 binary64)) (fma.f64 x x y)))
(+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x y)) (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (neg.f64 y) y)) (fma.f64 x x y)))
(*.f64 (/.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 x #s(literal 12 binary64))) (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 x x y))
(.f64 (/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 x x y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64)))) (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 x x y))
(.f64 (/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 x x y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64))) (+.f64 (pow.f64 (*.f64 (fma.f64 x x y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64)))) (fma.f64 x x y))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (fma.f64 x x y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64)))) (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 x x y)))
(.f64 (/.f64 (fma.f64 x x y) (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)))) (/.f64 (-.f64 (.f64 x x) (neg.f64 y)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (/.f64 (fma.f64 x x y) (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)))) (/.f64 (fma.f64 x x y) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(.f64 (/.f64 (fma.f64 x x y) (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (.f64 (fma.f64 x x y) y) #s(literal 3 binary64))))) (/.f64 (-.f64 (.f64 x x) (neg.f64 y)) (fma.f64 (.f64 (fma.f64 x x y) y) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(.f64 (/.f64 (fma.f64 x x y) (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (.f64 (fma.f64 x x y) y) #s(literal 3 binary64))))) (/.f64 (fma.f64 x x y) (fma.f64 (*.f64 (fma.f64 x x y) y) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(.f64 (/.f64 (fma.f64 x x y) (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))))) (/.f64 (-.f64 (.f64 x x) (neg.f64 y)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (/.f64 (fma.f64 x x y) (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))))) (/.f64 (fma.f64 x x y) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(.f64 (/.f64 (fma.f64 x x y) (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))) (/.f64 (-.f64 (.f64 x x) (neg.f64 y)) (fma.f64 x x y)))
(*.f64 (/.f64 (fma.f64 x x y) (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))) (/.f64 (fma.f64 x x y) (fma.f64 x x y)))
(.f64 (/.f64 (fma.f64 x x y) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (-.f64 (.f64 x x) (neg.f64 y)) (/.f64 (fma.f64 x x y) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))))
(*.f64 (/.f64 (fma.f64 x x y) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (fma.f64 x x y) (/.f64 (fma.f64 x x y) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))))
(.f64 (/.f64 (fma.f64 x x y) (fma.f64 x x y)) (/.f64 (-.f64 (.f64 x x) (neg.f64 y)) (/.f64 (fma.f64 x x y) (fma.f64 x x y))))
(*.f64 (/.f64 (fma.f64 x x y) (fma.f64 x x y)) (/.f64 (fma.f64 x x y) (/.f64 (fma.f64 x x y) (fma.f64 x x y))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))
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(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 x (fma.f64 x x y)) (/.f64 (*.f64 (neg.f64 (neg.f64 y)) (neg.f64 y)) (fma.f64 x x y)))
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(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (fma.f64 x x y)) (*.f64 y (/.f64 y (fma.f64 x x y))))
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(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (.f64 x x) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (.f64 (*.f64 (neg.f64 y) y) y) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
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(fma.f64 y (/.f64 y (fma.f64 x x y)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)))
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(-.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 x x y) (*.f64 y y)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64))))
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(-.f64 (/.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 3 binary64))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 3 binary64))))
(-.f64 (/.f64 (pow.f64 x #s(literal 18 binary64)) (.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 x #s(literal 12 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))) (/.f64 (pow.f64 y #s(literal 9 binary64)) (.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 x #s(literal 12 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))))
(-.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64))) (fma.f64 x x y)) (/.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64))) (fma.f64 x x y)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (+.f64 (pow.f64 (.f64 (fma.f64 x x y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64)))) (fma.f64 x x y)) (/.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (+.f64 (pow.f64 (.f64 (fma.f64 x x y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64)))) (fma.f64 x x y)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 18 binary64)) (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (/.f64 (pow.f64 y #s(literal 9 binary64)) (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (.f64 (+.f64 (pow.f64 (.f64 (fma.f64 x x y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64))) (fma.f64 x x y))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (.f64 (+.f64 (pow.f64 (.f64 (fma.f64 x x y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64))) (fma.f64 x x y))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 y y (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 y x) x)))) (/.f64 (.f64 (neg.f64 (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 y #s(literal 3/2 binary64))) (fma.f64 y y (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (*.f64 y x) x)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 y y (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 y x) x)))) (/.f64 (.f64 (.f64 (neg.f64 y) y) y) (fma.f64 y y (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 y x) x)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 y y (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 y x) x)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 y x) x)))))
(-.f64 (*.f64 y (/.f64 y (fma.f64 x x y))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) (/.f64 (*.f64 (neg.f64 (neg.f64 y)) y) (fma.f64 x x y)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) (/.f64 (*.f64 (neg.f64 (neg.f64 y)) (neg.f64 y)) (fma.f64 x x y)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) (*.f64 y (/.f64 y (fma.f64 x x y))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (*.f64 (neg.f64 (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 y #s(literal 3/2 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 (neg.f64 y) y) y) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (*.f64 x x) y)
(-.f64 y (*.f64 x x))
(+.f64 (/.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 3 binary64))) (/.f64 (.f64 (.f64 (neg.f64 y) y) (*.f64 y y)) (pow.f64 (fma.f64 x x y) #s(literal 3 binary64))))
(+.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))))
(+.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (.f64 (+.f64 (pow.f64 (.f64 (fma.f64 x x y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64))) (fma.f64 x x y))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (.f64 (+.f64 (pow.f64 (.f64 (fma.f64 x x y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64))) (fma.f64 x x y))))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 y x) x)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 y y (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 y x) x)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 y y (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 y x) x)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 y x) x)))))
(+.f64 (*.f64 y (/.f64 y (fma.f64 x x y))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) (/.f64 (*.f64 (neg.f64 (neg.f64 y)) (neg.f64 y)) (fma.f64 x x y)))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) (*.f64 y (/.f64 y (fma.f64 x x y))))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (*.f64 (neg.f64 (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 y #s(literal 3/2 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 (neg.f64 y) y) y) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (*.f64 x x) (neg.f64 y))
(+.f64 (*.f64 x x) y)
(+.f64 (neg.f64 y) (*.f64 x x))
(+.f64 y (*.f64 x x))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (-.f64 (.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64)))) (.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64)))))))
(neg.f64 (*.f64 x x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 x x))
(exp.f64 (/.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))

eval26.0ms (0.7%)

Memory: 2.9MiB live, 46.2MiB allocated
Compiler: Compiled 7 898 to 782 computations (90.1% saved)

prune4.0ms (0.1%)

Memory

13.3MiB live, 13.3MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	242	3	245
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	243	3	246

Accuracy

100.0%

Counts

246 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y)))
▶	52.1%	#s(approx (* 1/2 (- (* x x) y)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
▶	50.5%	#s(approx (* 1/2 (- (* x x) y)) (*.f64 #s(literal -1/2 binary64) y))

Status

Accuracy

Program

▶

100.0%

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

▶

52.1%

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

▶

50.5%

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

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify8.0ms (0.2%)

Memory

15.8MiB live, 15.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	56
0	21	56
1	37	56
2	80	56
3	161	56
4	232	56
5	251	56
6	261	56
7	271	56
8	281	56
0	281	56

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize64.0ms (1.7%)

Memory

-27.1MiB live, 19.5MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 x x (neg.f64 y))
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y)))
accuracy	0.0	(neg.f64 y)
accuracy	0.0	(.f64 (.f64 x x) #s(literal 1/2 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	30.649140980660516	#s(approx (* 1/2 (- (* x x) y)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
accuracy	0.0	(*.f64 #s(literal -1/2 binary64) y)
accuracy	31.682140966606568	#s(approx (* 1/2 (- (* x x) y)) (*.f64 #s(literal -1/2 binary64) y))

Samples

57.0ms

256×

valid

Compiler

Compiled 50 to 14 computations (72% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-mult: 43.0ms (91.8% of total)

ival-sub: 1.0ms (2.1% of total)

ival-add: 1.0ms (2.1% of total)

ival-neg: 1.0ms (2.1% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

3.2MiB live, 3.2MiB allocated

Counts

8 → 13

Calls

Call 1

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

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

Calls

6 calls:

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

simplify239.0ms (6.2%)

Memory

18.8MiB live, 248.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	74
1	109	66
2	362	66
3	1515	66
4	4450	66
5	6333	66
6	6944	66
7	7242	66
0	8543	66

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 13

Calls

Call 1

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

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

rewrite245.0ms (6.3%)

Memory

-28.1MiB live, 83.3MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	49
0	21	49
1	62	49
2	389	49
3	4301	44
0	8612	44

Stop Event

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

Counts

8 → 157

Calls

Call 1

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

Outputs
#s(approx (* 1/2 (- (* x x) y)) (*.f64 #s(literal -1/2 binary64) y))
(*.f64 #s(literal -1/2 binary64) y)
(*.f64 y #s(literal -1/2 binary64))
(*.f64 y #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) y)
(neg.f64 (*.f64 #s(literal -1/2 binary64) y))
(sqrt.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)))
(fabs.f64 (*.f64 #s(literal -1/2 binary64) y))
#s(approx (* 1/2 (- (* x x) y)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(.f64 (fabs.f64 (.f64 x #s(literal 1/2 binary64))) x)
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 x #s(literal 1/2 binary64)) x)
(.f64 x (fabs.f64 (.f64 x #s(literal 1/2 binary64))))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(neg.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))))
(fabs.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 x x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 x x))
(exp.f64 (/.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/2 binary64)) (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (.f64 (fma.f64 x x y) y) #s(literal 3 binary64)))) (fma.f64 (.f64 (fma.f64 x x y) y) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(.f64 (/.f64 (.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64))) (fma.f64 x x y))
(.f64 (/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 x x y)))
(*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/2 binary64) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (fma.f64 x x y) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x x y))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (.f64 (fma.f64 x x y) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64))))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) y) (*.f64 (fma.f64 x x y) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (fma.f64 x x y))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/2 binary64)))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (neg.f64 (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)) (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 6 binary64)))))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (fma.f64 x x y) #s(literal 1/2 binary64))) (.f64 (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 y y)))) (pow.f64 (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)))) (.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)))) (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64))))) (.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 (fma.f64 x x y) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) y) (*.f64 (fma.f64 x x y) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (*.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (fma.f64 x x y))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/2 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))
(/.f64 (neg.f64 (pow.f64 (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (neg.f64 (.f64 (fma.f64 x x y) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)) (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 y y) (-.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) y)))))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)) (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 (fma.f64 x x y) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 x x y))
(/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/2 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))
(/.f64 (pow.f64 (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)) (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal 1/4 binary64) (.f64 y y) (-.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) y))))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)) (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 (fma.f64 x x y) #s(literal 1/2 binary64)))))
(fma.f64 (fabs.f64 (.f64 x #s(literal 1/2 binary64))) x (.f64 #s(literal -1/2 binary64) y))
(fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64) (*.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) y))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) y))
(fma.f64 #s(literal -1/2 binary64) y (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 y #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 y #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 x (fabs.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 #s(literal -1/2 binary64) y))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal -1/2 binary64) y))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 #s(literal -1/2 binary64) y))
(fma.f64 #s(literal 1/2 binary64) y (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (fma.f64 x x y) #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (*.f64 (fma.f64 x x y) #s(literal 1/2 binary64))))
(-.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(-.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(-.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) (*.f64 #s(literal -1/2 binary64) y))
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(sqrt.f64 (*.f64 y y))
(fabs.f64 y)
(exp.f64 (/.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 y) #s(literal 1 binary64)))
(exp.f64 (log.f64 y))
(+.f64 (cosh.f64 (log.f64 y)) (sinh.f64 (log.f64 y)))
y

eval16.0ms (0.4%)

Memory: 16.1MiB live, 16.1MiB allocated
Compiler: Compiled 3 660 to 493 computations (86.5% saved)

prune4.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	161	4	165

Accuracy

100.0%

Counts

165 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y)))
✓	52.1%	#s(approx (* 1/2 (- (* x x) y)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
▶	2.2%	#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal 1/2 binary64)))
✓	50.5%	#s(approx (* 1/2 (- (* x x) y)) (*.f64 #s(literal -1/2 binary64) y))

Compiler

Compiled 42 to 34 computations (19% saved)

simplify4.0ms (0.1%)

Memory

1.6MiB live, 1.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
0	9	16
1	15	16
2	28	16
3	47	16
4	59	16
0	59	16

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize150.0ms (3.9%)

Memory

-36.5MiB live, 10.1MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(*.f64 y #s(literal 1/2 binary64))
accuracy	62.579869441262055	#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal 1/2 binary64)))

Samples

146.0ms

256×

valid

Compiler

Compiled 14 to 9 computations (35.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 140.0ms

ival-mult: 138.0ms (98.7% of total)

ival-sub: 1.0ms (0.7% 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

1.7MiB live, 1.7MiB allocated

Counts

2 → 7

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	y	@	-inf	((* 1/2 (- (* x x) y)) (* y 1/2))
0.0ms	y	@	inf	((* 1/2 (- (* x x) y)) (* y 1/2))
0.0ms	y	@	0	((* 1/2 (- (* x x) y)) (* y 1/2))
0.0ms	x	@	inf	((* 1/2 (- (* x x) y)) (* y 1/2))
0.0ms	x	@	-inf	((* 1/2 (- (* x x) y)) (* y 1/2))

simplify192.0ms (4.9%)

Memory

12.6MiB live, 107.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	47
1	62	39
2	188	39
3	685	39
4	3448	39
0	8540	39

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 7

Calls

Call 1

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

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

rewrite85.0ms (2.2%)

Memory

22.8MiB live, 162.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
0	9	14
1	30	14
2	198	14
3	2130	14
0	9308	13

Stop Event

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

Counts

2 → 3

Calls

Call 1

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

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

eval1.0ms (0%)

Memory: 2.3MiB live, 2.3MiB allocated
Compiler: Compiled 87 to 24 computations (72.4% saved)

prune2.0ms (0.1%)

Memory

5.3MiB live, 5.3MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	7	0	7
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	7	4	11

Accuracy

100.0%

Counts

11 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y)))
✓	52.1%	#s(approx (* 1/2 (- (* x x) y)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
✓	2.2%	#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal 1/2 binary64)))
✓	50.5%	#s(approx (* 1/2 (- (* x x) y)) (*.f64 #s(literal -1/2 binary64) y))

Compiler

Compiled 91 to 54 computations (40.7% saved)

regimes48.0ms (1.2%)

Memory

1.1MiB live, 48.5MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

5 calls:

39.0ms	x
2.0ms	y
2.0ms	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
2.0ms	(-.f64 (*.f64 x x) y)
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	1	`(*.f64 x x)`
100.0%	1	`(-.f64 (*.f64 x x) y)`
100.0%	1	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
100.0%	1	`x`
100.0%	1	`y`

Compiler

Compiled 17 to 17 computations (0% saved)

regimes31.0ms (0.8%)

Memory

-7.6MiB live, 32.2MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

22.0ms	x
3.0ms	(*.f64 x x)
2.0ms	y
2.0ms	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
2.0ms	(-.f64 (*.f64 x x) y)

Results

Accuracy	Segments	Branch
100.0%	1	`(*.f64 x x)`
100.0%	1	`(-.f64 (*.f64 x x) y)`
100.0%	1	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
100.0%	1	`x`
100.0%	1	`y`

Compiler

Compiled 17 to 17 computations (0% saved)

regimes8.0ms (0.2%)

Memory

20.3MiB live, 20.3MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

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

Calls

5 calls:

2.0ms	y
2.0ms	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
2.0ms	x
2.0ms	(-.f64 (*.f64 x x) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
88.0%	2	`(*.f64 x x)`
82.5%	2	`(-.f64 (*.f64 x x) y)`
82.5%	2	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
88.0%	2	`x`
65.5%	3	`y`

Compiler

Compiled 17 to 17 computations (0% saved)

regimes19.0ms (0.5%)

Memory

-32.4MiB live, 15.7MiB allocated

Accuracy

Total -31.4b remaining (-99.1%)

Threshold costs -31.4b (-99.1%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

5 calls:

14.0ms	x
1.0ms	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
1.0ms	y
1.0ms	(-.f64 (*.f64 x x) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
50.5%	1	`y`
50.5%	1	`(-.f64 (*.f64 x x) y)`
50.5%	1	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
50.5%	1	`(*.f64 x x)`
50.5%	1	`x`

Compiler

Compiled 17 to 17 computations (0% saved)

bsearch9.0ms (0.2%)

Memory

12.8MiB live, 12.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
7.0ms	0.04264995278084728	0.2412986389596484

Samples

4.0ms

96×

valid

Compiler

Compiled 154 to 137 computations (11% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-mult: 1.0ms (54.6% of total)

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

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

exact: 0.0ms (0% of total)

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

simplify10.0ms (0.3%)

Memory

16.9MiB live, 16.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	53
1	31	53
2	45	53
3	64	53
4	76	53

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y)))
(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
(if (<=.f64 x #s(literal 7566047373982433/72057594037927936 binary64)) #s(approx (* 1/2 (- (* x x) y)) (.f64 #s(literal -1/2 binary64) y)) #s(approx ( 1/2 (- (* x x) y)) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (- (* x x) y)) (*.f64 #s(literal -1/2 binary64) y))

Outputs
(*.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y)))
(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
(if (<=.f64 x #s(literal 7566047373982433/72057594037927936 binary64)) #s(approx (* 1/2 (- (* x x) y)) (.f64 #s(literal -1/2 binary64) y)) #s(approx ( 1/2 (- (* x x) y)) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (- (* x x) y)) (*.f64 #s(literal -1/2 binary64) y))

soundness1.0s (26.9%)

Memory

5.1MiB live, 334.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	74
1	109	66
2	362	66
3	1514	66
4	4452	66
5	6334	66
6	6943	66
7	7241	66
0	8542	66
0	6	15
0	9	15
1	29	15
2	197	15
3	2129	15
0	9773	13

Stop Event

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

Compiler

Compiled 64 to 34 computations (46.9% saved)

preprocess26.0ms (0.7%)

Memory: -22.7MiB live, 69.5MiB allocated
Remove: (abs x)
Compiler: Compiled 148 to 78 computations (47.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	15	56
0	21	56
1	37	56
2	80	56
3	161	56
4	232	56
5	251	56
6	261	56
7	271	56
8	281	56
0	281	56

Iter	Nodes	Cost
0	15	56
0	21	56
1	37	56
2	80	56
3	161	56
4	232	56
5	251	56
6	261	56
7	271	56
8	281	56
0	281	56

start0.0ms (0%)

analyze0.0ms (0%)

sample879.0ms (22.7%)

explain111.0ms (2.9%)

preprocess88.0ms (2.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize15.0ms (0.4%)

series30.0ms (0.8%)

simplify260.0ms (6.7%)

rewrite252.0ms (6.5%)

eval26.0ms (0.7%)

prune4.0ms (0.1%)

simplify8.0ms (0.2%)

localize64.0ms (1.7%)

series4.0ms (0.1%)

simplify239.0ms (6.2%)

rewrite245.0ms (6.3%)

eval16.0ms (0.4%)

prune4.0ms (0.1%)

simplify4.0ms (0.1%)

localize150.0ms (3.9%)

series2.0ms (0.1%)

simplify192.0ms (4.9%)

rewrite85.0ms (2.2%)

eval1.0ms (0%)

prune2.0ms (0.1%)

regimes48.0ms (1.2%)

regimes31.0ms (0.8%)

regimes8.0ms (0.2%)

regimes19.0ms (0.5%)

bsearch9.0ms (0.2%)

simplify10.0ms (0.3%)

soundness1.0s (26.9%)

preprocess26.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	15	56
0	21	56
1	37	56
2	80	56
3	161	56
4	232	56
5	251	56
6	261	56
7	271	56
8	281	56
0	281	56