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

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB 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)

sample532.0ms (10.6%)

Memory

50.4MiB live, 702.0MiB allocated

Samples

346.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 170.0ms

ival-mult: 122.0ms (71.8% of total)

ival-sub: 37.0ms (21.8% of total)

ival-true: 4.0ms (2.4% of total)

exact: 4.0ms (2.4% of total)

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

Bogosity

preprocess47.0ms (0.9%)

Memory

-18.6MiB live, 59.3MiB allocated

Algorithm

1×	egg-herbie

Rules

336×	`accelerator-lowering-fma.f32`
336×	`accelerator-lowering-fma.f64`
216×	`-lowering-.f32`
216×	`-lowering-.f64`
200×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	37
1	46	35
2	129	35
3	381	35
4	678	35
5	844	35
6	882	35
7	882	35
0	6	7
1	9	7
2	20	7
3	42	7
4	67	7
5	95	7
6	165	7
7	264	7
8	410	7
9	465	7
10	499	7
0	499	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Symmetry

(abs x)

explain79.0ms (1.6%)

Memory

27.7MiB live, 66.2MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`*.f64`	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`	*no**	1	0

Confusion

	Predicted +	Predicted -
+	1	0
-	0	255

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	255

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	255
1	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

22.0ms

512×

valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

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

ival-mult: 6.0ms (64.2% of total)

ival-sub: 2.0ms (21.4% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune32.0ms (0.6%)

Memory

-42.4MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify18.0ms (0.4%)

Memory

22.1MiB live, 22.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

336×	`accelerator-lowering-fma.f32`
336×	`accelerator-lowering-fma.f64`
216×	`-lowering-.f32`
216×	`-lowering-.f64`
80×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	9	18
2	20	18
3	42	18
4	67	18
5	95	18
6	165	18
7	264	18
8	410	18
9	465	18
10	499	18
0	499	18

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize20.0ms (0.4%)

Memory

-2.9MiB live, 34.6MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(-.f64 (*.f64 x x) y)
✓	accuracy	99.7%	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))

Samples

12.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-mult: 3.0ms (49.2% of total)

ival-sub: 2.0ms (32.8% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

6.1MiB live, 6.1MiB allocated

Counts

3 → 60

Calls

Call 1

Inputs
#<alt (* 1/2 (- (* x x) y))>
#<alt (- (* x x) y)>
#<alt (* x x)>

Outputs
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (* -1/2 y)>
#<alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2))>
#<alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2))>
#<alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))>
#<alt (* -1 y)>
#<alt (- (pow x 2) y)>
#<alt (- (pow x 2) y)>
#<alt (- (pow x 2) y)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))>
#<alt (pow x 2)>
#<alt (+ (* -1 y) (pow x 2))>
#<alt (+ (* -1 y) (pow x 2))>
#<alt (+ (* -1 y) (pow x 2))>
#<alt (* -1 y)>
#<alt (* y (- (/ (pow x 2) y) 1))>
#<alt (* y (- (/ (pow x 2) y) 1))>
#<alt (* y (- (/ (pow x 2) y) 1))>
#<alt (* -1 y)>
#<alt (* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

15 calls:

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

rewrite544.0ms (10.8%)

Memory

-6.6MiB live, 440.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 946×	`accelerator-lowering-fma.f32`
6 946×	`accelerator-lowering-fma.f64`
4 110×	`/-lowering-/.f32`
4 110×	`/-lowering-/.f64`
3 550×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	24	15
2	175	15
3	1640	15
0	8545	15

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 266

Calls

Call 1

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

Outputs
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (*.f64 #s(literal -1/2 binary64) y))
(+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (*.f64 y #s(literal 1/2 binary64)))
(-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (*.f64 #s(literal 1/2 binary64) y))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal -1/2 binary64) y))) (/.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal -1/2 binary64) y))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 #s(literal -1/2 binary64) y))
(fma.f64 #s(literal 1/2 binary64) (neg.f64 y) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal -1/2 binary64) y))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) y))
(fma.f64 (neg.f64 y) #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(fma.f64 #s(literal -1 binary64) (.f64 y #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(fma.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal -1/2 binary64) y))
(fma.f64 #s(literal -1/2 binary64) y (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) y)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) y)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal -1/2 binary64) y)))) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/8 binary64) (.f64 (.f64 y (*.f64 y y)) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal -1/2 binary64) y)) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64)) (.f64 (*.f64 y y) #s(literal 1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (fma.f64 x x y)))) (.f64 #s(literal 1/2 binary64) (neg.f64 (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 y (.f64 y y)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (fma.f64 x x y)) (.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 x x y) (neg.f64 (-.f64 (*.f64 x x) y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (fma.f64 x x y)))) (.f64 (neg.f64 (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 y (.f64 y y)))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (fma.f64 x x y)) (.f64 (.f64 (fma.f64 x x y) (neg.f64 (-.f64 (*.f64 x x) y))) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 y (.f64 y y)))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (fma.f64 x x y))))
(/.f64 (.f64 (fma.f64 x x y) (.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))) (fma.f64 x x y))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 y (.f64 y y))))) (neg.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (fma.f64 x x y)))))
(/.f64 (neg.f64 (.f64 (fma.f64 x x y) (.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)))) (neg.f64 (fma.f64 x x y)))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/8 binary64) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (*.f64 #s(literal -1/2 binary64) y)))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64)) (.f64 (.f64 y y) #s(literal 1/4 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (*.f64 #s(literal -1/2 binary64) y)))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) y))))
(/.f64 (.f64 #s(literal 1/2 binary64) (neg.f64 (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 y (.f64 y y))))) (neg.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (fma.f64 x x y)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 x x y) (neg.f64 (-.f64 (*.f64 x x) y)))) (neg.f64 (fma.f64 x x y)))
(/.f64 (.f64 (neg.f64 (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 y (.f64 y y)))) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (fma.f64 x x y)))))
(/.f64 (.f64 (.f64 (fma.f64 x x y) (neg.f64 (-.f64 (*.f64 x x) y))) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 x x y)))
(/.f64 (/.f64 (.f64 (fma.f64 x x y) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))) (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)))
(/.f64 (neg.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 y (.f64 y y)))))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (fma.f64 x x y))))
(/.f64 (neg.f64 (neg.f64 (.f64 (fma.f64 x x y) (.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))))) (fma.f64 x x y))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/8 binary64) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (*.f64 #s(literal -1/2 binary64) y))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64)) (.f64 (.f64 y y) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (*.f64 #s(literal -1/2 binary64) y))))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (neg.f64 (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 y (.f64 y y)))))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (fma.f64 x x y))))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 x x y) (neg.f64 (-.f64 (*.f64 x x) y))))) (fma.f64 x x y))
(/.f64 (neg.f64 (.f64 (neg.f64 (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 y (.f64 y y)))) #s(literal 1/2 binary64))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (fma.f64 x x y))))
(/.f64 (neg.f64 (.f64 (.f64 (fma.f64 x x y) (neg.f64 (-.f64 (*.f64 x x) y))) #s(literal 1/2 binary64))) (fma.f64 x x y))
(/.f64 (fma.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/8 binary64))) (fma.f64 (.f64 y y) #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
(/.f64 (-.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64))) (-.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))) #s(literal -1 binary64))
(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
(.f64 (-.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(.f64 (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 y (.f64 y y))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 x x)) (*.f64 y (fma.f64 x x y)))) #s(literal 1/2 binary64)))
(.f64 (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 y (.f64 y y))) (/.f64 #s(literal 1/2 binary64) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (fma.f64 x x y)))))
(.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #s(literal 1/2 binary64)))
(.f64 (.f64 (-.f64 (*.f64 x x) y) (fma.f64 x x y)) (/.f64 #s(literal 1/2 binary64) (fma.f64 x x y)))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)))
(.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 x x)) (*.f64 y (fma.f64 x x y)))))
(.f64 (.f64 (fma.f64 x x y) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))) (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))
(.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 y (.f64 y y))))) (/.f64 #s(literal -1 binary64) (fma.f64 x (.f64 x (.f64 x x)) (*.f64 y (fma.f64 x x y)))))
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simplify179.0ms (3.6%)

Memory

19.7MiB live, 291.8MiB allocated

Algorithm

1×	egg-herbie

Rules

5 028×	`accelerator-lowering-fma.f32`
5 028×	`accelerator-lowering-fma.f64`
3 454×	`-lowering-.f32`
3 454×	`-lowering-.f64`
1 366×	`div-sub`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	327
1	102	327
2	297	327
3	993	291
4	2493	291
5	4972	291
6	7159	291
0	8120	291

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

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

eval37.0ms (0.7%)

Memory: 1.9MiB live, 81.7MiB allocated
Compiler: Compiled 14 301 to 904 computations (93.7% saved)

prune36.0ms (0.7%)

Memory

-0.1MiB live, 77.2MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	322	4	326
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	323	4	327

Accuracy

100.0%

Counts

327 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal -1/2 binary64) y))
▶	99.7%	(*.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y)))
▶	51.0%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
▶	50.3%	(*.f64 #s(literal -1/2 binary64) y)

Compiler

Compiled 31 to 22 computations (29% saved)

simplify30.0ms (0.6%)

Memory

-35.1MiB live, 19.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal -1/2 binary64) y)
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	192	(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal -1/2 binary64) y))
✓	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 #s(literal 1/2 binary64) (.f64 x x))
✓	cost-diff	0	(*.f64 #s(literal -1/2 binary64) y)

Rules

336×	`accelerator-lowering-fma.f32`
336×	`accelerator-lowering-fma.f64`
216×	`-lowering-.f32`
216×	`-lowering-.f64`
80×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	49
1	31	49
2	45	49
3	68	49
4	96	49
5	166	49
6	262	49
7	406	49
8	462	49
9	494	49
0	494	49

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize62.0ms (1.2%)

Memory

-0.9MiB live, 73.3MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal -1/2 binary64) y))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal -1/2 binary64) y)
✓	accuracy	100.0%	(fma.f64 x x (neg.f64 y))
✓	accuracy	100.0%	(neg.f64 y)
✓	accuracy	99.7%	(*.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.7%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	accuracy	100.0%	(*.f64 #s(literal -1/2 binary64) y)

Samples

23.0ms

256×

valid

Compiler

Compiled 52 to 15 computations (71.2% saved)

Precisions

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

ival-mult: 8.0ms (65.8% of total)

ival-add: 2.0ms (16.4% of total)

ival-neg: 1.0ms (8.2% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

8 → 132

Calls

Call 1

Inputs
#<alt (* -1/2 y)>
#<alt (* 1/2 (* x x))>
#<alt (* x x)>
#<alt (* 1/2 (+ (* x x) (neg y)))>
#<alt (+ (* x x) (neg y))>
#<alt (neg y)>
#<alt (+ (* (* 1/2 x) x) (* -1/2 y))>
#<alt (* 1/2 x)>

Outputs
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (* -1/2 y)>
#<alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2))>
#<alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2))>
#<alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))>
#<alt (* -1 y)>
#<alt (- (pow x 2) y)>
#<alt (- (pow x 2) y)>
#<alt (- (pow x 2) y)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))>
#<alt (pow x 2)>
#<alt (+ (* -1 y) (pow x 2))>
#<alt (+ (* -1 y) (pow x 2))>
#<alt (+ (* -1 y) (pow x 2))>
#<alt (* -1 y)>
#<alt (* y (- (/ (pow x 2) y) 1))>
#<alt (* y (- (/ (pow x 2) y) 1))>
#<alt (* y (- (/ (pow x 2) y) 1))>
#<alt (* -1 y)>
#<alt (* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (+ (* -1/2 y) (* 1/2 (pow x 2)))>
#<alt (* -1/2 y)>
#<alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2))>
#<alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2))>
#<alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>

Calls

33 calls:

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

rewrite449.0ms (8.9%)

Memory

21.1MiB live, 453.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 528×	`accelerator-lowering-fma.f32`
6 528×	`accelerator-lowering-fma.f64`
5 214×	`-lowering-.f32`
5 214×	`-lowering-.f64`
1 966×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	58	35
2	443	35
3	4393	34
0	10602	31

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 454

Calls

Call 1

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

Outputs
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) y))
(exp.f64 (log.f64 (*.f64 #s(literal -1/2 binary64) y)))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal -1/2 binary64) y)) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) y))
(neg.f64 (*.f64 #s(literal -1/2 binary64) y))
(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 y y)) y)
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y (.f64 y y))) (.f64 y y))
(/.f64 (.f64 (.f64 y (.f64 y y)) #s(literal 1/2 binary64)) (.f64 y y))
(/.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -1/2 binary64)) (.f64 y y))
(pow.f64 (*.f64 #s(literal -1/2 binary64) y) #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) y)
(*.f64 y #s(literal -1/2 binary64))
(*.f64 y #s(literal 1/2 binary64))
(*.f64 y (exp.f64 (log.f64 #s(literal 1/2 binary64))))
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(.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x x y)) (/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x x y)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x y))))
(.f64 (fma.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64) (neg.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/8 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x y)))))))
(.f64 (neg.f64 (.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 x x y) (fma.f64 x x y)))) (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x x y)))))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (fma.f64 x x y)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (fma.f64 x x y))) (.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 x x y) (fma.f64 x x y))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x y))))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64))))
(.f64 (.f64 #s(literal 1/4 binary64) (neg.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 y (*.f64 x x)))))
(.f64 (.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x y) (.f64 y y)) (fma.f64 x x y))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x y) (*.f64 y y))))
(.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 x x y) (fma.f64 x x y))) (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))
(.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x x y)) (fma.f64 x x y)) (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x x y)) #s(literal 1/2 binary64)))
(.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x x y)) #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x x y)) (fma.f64 x x y)))
(.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x x y)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64)))) (/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x x y)) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x y)))))))
(.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 x x y) (fma.f64 x x y))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64)))) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x y)))))
(.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 x x y) (fma.f64 x x y))) (.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 x x y) (fma.f64 x x y)))) (.f64 #s(literal 1/2 binary64) (fma.f64 x x y)))
(.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 x x y) (fma.f64 x x y))) (fma.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64) (neg.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/8 binary64))))) (neg.f64 (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x y))))))
(.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 x x y) (fma.f64 x x y))) (neg.f64 (.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 x x y) (fma.f64 x x y))))) (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x x y))))
(.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 x x y) (fma.f64 x x y))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (fma.f64 x x y))))
(.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 x x y) (fma.f64 x x y))) (.f64 #s(literal 1/4 binary64) (neg.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y))))) (.f64 #s(literal 1/2 binary64) (-.f64 y (*.f64 x x))))
(.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 x x y) (fma.f64 x x y))) (.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x y) (.f64 y y)) (fma.f64 x x y)))) (fma.f64 (.f64 x x) (fma.f64 x x y) (*.f64 y y)))
(.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 x x y) (fma.f64 x x y))) (.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 x x y) (fma.f64 x x y)))) (fma.f64 x x y))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64))) (fma.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64)) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (-.f64 y (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/64 binary64))))) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (fma.f64 x x y))) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (fma.f64 x x y))) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/16 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64))) (fma.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 x x y) (fma.f64 x x y))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/16 binary64)))) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x y)))))
(.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x y) (.f64 y y)) (fma.f64 x x y))) (fma.f64 (.f64 y (fma.f64 x x y)) (.f64 (.f64 y y) (.f64 (fma.f64 x x y) (fma.f64 x x y))) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x))))))) (fma.f64 (.f64 y (fma.f64 x x y)) (-.f64 (.f64 y (fma.f64 x x y)) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))
(.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x y) (.f64 y y)) (fma.f64 x x y))) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x y) (.f64 y y)) (fma.f64 (.f64 x x) (fma.f64 x x y) (.f64 y y)))) (fma.f64 (.f64 x x) (fma.f64 x x y) (.f64 y y)))
(.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 x x y) (fma.f64 x x y))) (.f64 (fma.f64 x x y) (fma.f64 x x y))) (fma.f64 x x y))
(.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 x x y) (fma.f64 x x y))) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x y) (.f64 y y)) (fma.f64 x x y))) (fma.f64 (.f64 x x) (fma.f64 x x y) (.f64 y y)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))

simplify258.0ms (5.1%)

Memory

-28.8MiB live, 288.9MiB allocated

Algorithm

1×	egg-herbie

Rules

5 028×	`accelerator-lowering-fma.f32`
5 028×	`accelerator-lowering-fma.f64`
3 454×	`-lowering-.f32`
3 454×	`-lowering-.f64`
1 368×	`div-sub`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	669
1	104	669
2	297	669
3	988	597
4	2491	597
5	4971	597
6	7141	597
0	8103	597

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

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

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

eval69.0ms (1.4%)

Memory: 32.5MiB live, 146.4MiB allocated
Compiler: Compiled 14 577 to 934 computations (93.6% saved)

prune48.0ms (0.9%)

Memory

-3.3MiB live, 110.7MiB allocated

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	618	2	620
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	620	4	624

Accuracy

100.0%

Counts

624 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.3%	(.f64 (.f64 #s(literal 1/2 binary64) x) x)
▶	2.1%	(*.f64 y #s(literal 1/2 binary64))
✓	99.7%	(*.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y)))
✓	50.3%	(*.f64 #s(literal -1/2 binary64) y)

Compiler

Compiled 26 to 19 computations (26.9% saved)

simplify3.0ms (0.1%)

Memory

5.0MiB live, 5.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

18×	`-lowering-.f32`
18×	`-lowering-.f64`
6×	`*-commutative`
2×	`associate-r`
2×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	11	15
2	12	15
0	12	15

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize134.0ms (2.7%)

Memory

-16.0MiB live, 29.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 #s(literal 1/2 binary64) x) x)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(*.f64 y #s(literal 1/2 binary64))

Samples

127.0ms

256×

valid

Compiler

Compiled 17 to 8 computations (52.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 121.0ms

ival-mult: 120.0ms (99.3% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (* y 1/2)>
#<alt (* (* 1/2 x) x)>
#<alt (* 1/2 x)>

Outputs
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>

Calls

9 calls:

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

rewrite681.0ms (13.5%)

Memory

-4.6MiB live, 166.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 136×	`pow-lowering-pow.f64`
2 136×	`pow-lowering-pow.f32`
1 592×	`-lowering-.f32`
1 592×	`-lowering-.f64`
1 412×	`prod-exp`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	11	13
2	14	13
3	21	13
4	36	13
5	92	13
6	281	5
7	1668	5
8	1693	5
9	1816	5
10	3070	5
0	8421	5

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 4

Calls

Call 1

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

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

simplify5.0ms (0.1%)

Memory

11.0MiB live, 11.0MiB allocated

Algorithm

1×	egg-herbie

Rules

18×	`-lowering-.f32`
18×	`-lowering-.f64`
6×	`*-commutative`
2×	`pow-lowering-pow.f64`
2×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	132
1	12	132
2	14	132
0	14	132

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

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

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

eval6.0ms (0.1%)

Memory: -25.0MiB live, 12.6MiB allocated
Compiler: Compiled 168 to 9 computations (94.6% saved)

prune3.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	38	6	44

Accuracy

100.0%

Counts

44 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.3%	(.f64 (.f64 #s(literal 1/2 binary64) x) x)
✓	2.1%	(*.f64 y #s(literal 1/2 binary64))
✓	99.7%	(*.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y)))
▶	5.3%	(*.f64 #s(literal 1/2 binary64) x)
✓	50.3%	(*.f64 #s(literal -1/2 binary64) y)
▶	3.8%	#s(literal 1/2 binary64)

Compiler

Compiled 34 to 26 computations (23.5% saved)

simplify3.0ms (0.1%)

Memory

5.7MiB live, 5.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

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

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	6
1	4	6
0	4	6

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize14.0ms (0.3%)

Memory

-11.8MiB live, 26.3MiB allocated

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)

Samples

7.0ms

256×

valid

Compiler

Compiled 8 to 6 computations (25% saved)

Precisions

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

ival-mult: 2.0ms (100.7% of total)

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

exact: 0.0ms (0% of total)

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

series0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (* 1/2 x)>

Outputs
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>

Calls

3 calls:

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

rewrite7.0ms (0.1%)

Memory

15.9MiB live, 15.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	4	3
0	4	3

Stop Event

1×	iter limit
1×	saturated

Counts

1 → 2

Calls

Call 1

Inputs
(* 1/2 x)

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

simplify3.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	36
1	4	36
0	4	36

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

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

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

eval1.0ms (0%)

Memory: 3.5MiB live, 3.5MiB allocated
Compiler: Compiled 44 to 5 computations (88.6% saved)

prune5.0ms (0.1%)

Memory

-28.5MiB live, 9.8MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	14	6	20

Accuracy

100.0%

Counts

20 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.3%	(.f64 (.f64 #s(literal 1/2 binary64) x) x)
✓	2.1%	(*.f64 y #s(literal 1/2 binary64))
✓	99.7%	(*.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y)))
✓	5.3%	(*.f64 #s(literal 1/2 binary64) x)
✓	50.3%	(*.f64 #s(literal -1/2 binary64) y)
✓	3.8%	#s(literal 1/2 binary64)

Compiler

Compiled 78 to 42 computations (46.2% saved)

regimes24.0ms (0.5%)

Memory

6.7MiB live, 47.6MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

5 calls:

9.0ms	x
3.0ms	y
3.0ms	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
3.0ms	(-.f64 (*.f64 x x) y)
3.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 27 to 17 computations (37% saved)

regimes20.0ms (0.4%)

Memory

18.7MiB live, 53.9MiB allocated

Counts

8 → 1

Calls

Call 1

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

7.0ms	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
3.0ms	y
3.0ms	(-.f64 (*.f64 x x) y)
3.0ms	x
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`y`
99.7%	1	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
99.7%	1	`(-.f64 (*.f64 x x) y)`
99.7%	1	`(*.f64 x x)`

Compiler

Compiled 27 to 17 computations (37% saved)

regimes15.0ms (0.3%)

Memory

8.2MiB live, 47.6MiB allocated

Counts

7 → 1

Calls

Call 1

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

4.0ms	(-.f64 (*.f64 x x) y)
3.0ms	y
3.0ms	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
3.0ms	x
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`y`
99.7%	1	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
99.7%	1	`(-.f64 (*.f64 x x) y)`
99.7%	1	`(*.f64 x x)`

Compiler

Compiled 27 to 17 computations (37% saved)

regimes14.0ms (0.3%)

Memory

3.7MiB live, 43.3MiB allocated

Counts

6 → 2

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
87.4%	2	`x`
68.6%	3	`y`
82.2%	4	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
82.2%	4	`(-.f64 (*.f64 x x) y)`
87.4%	2	`(*.f64 x x)`

Compiler

Compiled 27 to 17 computations (37% saved)

regimes9.0ms (0.2%)

Memory

-25.0MiB live, 17.5MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	(*.f64 x x)
2.0ms	x

Results

Accuracy	Segments	Branch
87.0%	2	`x`
87.0%	2	`(*.f64 x x)`

Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes11.0ms (0.2%)

Memory

27.8MiB live, 27.8MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
50.3%	1	`y`
50.3%	1	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
50.3%	1	`(-.f64 (*.f64 x x) y)`
50.3%	1	`x`
50.3%	1	`(*.f64 x x)`

Compiler

Compiled 27 to 17 computations (37% saved)

regimes7.0ms (0.1%)

Memory

-19.9MiB live, 19.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1/2 binary64)

Outputs
#s(literal 1/2 binary64)

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
3.8%	1	`y`
3.8%	1	`x`
3.8%	1	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
3.8%	1	`(-.f64 (*.f64 x x) y)`
3.8%	1	`(*.f64 x x)`

Compiler

Compiled 27 to 17 computations (37% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.2029133375224637e-80	4.480090931954136e-80

Compiler

Compiled 12 to 11 computations (8.3% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.2029133375224637e-80	4.480090931954136e-80

Compiler

Compiled 12 to 11 computations (8.3% saved)

simplify7.0ms (0.1%)

Memory

13.5MiB live, 13.5MiB allocated

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	54
1	30	54
2	33	54
3	34	54

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal -1/2 binary64) y))
(*.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 (.f64 x x) #s(literal 5339967589802275/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072 binary64)) (.f64 #s(literal -1/2 binary64) y) (.f64 (.f64 #s(literal 1/2 binary64) x) x))
(if (<=.f64 (.f64 x x) #s(literal 5339967589802275/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072 binary64)) (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(*.f64 #s(literal -1/2 binary64) y)
#s(literal 1/2 binary64)

Outputs
(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal -1/2 binary64) y))
(*.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 (.f64 x x) #s(literal 5339967589802275/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072 binary64)) (.f64 #s(literal -1/2 binary64) y) (.f64 (.f64 #s(literal 1/2 binary64) x) x))
(if (<=.f64 (.f64 x x) #s(literal 5339967589802275/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072 binary64)) (.f64 #s(literal -1/2 binary64) y) (.f64 x (.f64 #s(literal 1/2 binary64) x)))
(if (<=.f64 (.f64 x x) #s(literal 5339967589802275/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072 binary64)) (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(*.f64 #s(literal -1/2 binary64) y)
#s(literal 1/2 binary64)

soundness1.6s (31.3%)

Memory

-20.2MiB live, 420.7MiB allocated

Rules

6 946×	`accelerator-lowering-fma.f32`
6 946×	`accelerator-lowering-fma.f64`
6 528×	`accelerator-lowering-fma.f32`
6 528×	`accelerator-lowering-fma.f64`
5 214×	`-lowering-.f32`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	58	35
2	443	35
3	4393	34
0	10602	31
0	6	13
1	11	13
2	14	13
3	21	13
4	36	13
5	92	13
6	281	5
7	1668	5
8	1693	5
9	1816	5
10	3070	5
0	8421	5
0	6	15
1	24	15
2	175	15
3	1640	15
0	8545	15
0	35	327
1	102	327
2	297	327
3	993	291
4	2493	291
5	4972	291
6	7159	291
0	8120	291

Stop Event

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

Compiler

Compiled 125 to 69 computations (44.8% saved)

preprocess38.0ms (0.8%)

Memory: -2.4MiB live, 74.4MiB allocated
Remove: (abs x)
Compiler: Compiled 170 to 78 computations (54.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	16	37
1	46	35
2	129	35
3	381	35
4	678	35
5	844	35
6	882	35
7	882	35
0	6	7
1	9	7
2	20	7
3	42	7
4	67	7
5	95	7
6	165	7
7	264	7
8	410	7
9	465	7
10	499	7
0	499	7

Iter	Nodes	Cost
0	6	18
1	9	18
2	20	18
3	42	18
4	67	18
5	95	18
6	165	18
7	264	18
8	410	18
9	465	18
10	499	18
0	499	18

Iter	Nodes	Cost
0	13	49
1	31	49
2	45	49
3	68	49
4	96	49
5	166	49
6	262	49
7	406	49
8	462	49
9	494	49
0	494	49

Iter	Nodes	Cost
0	16	37
1	46	35
2	129	35
3	381	35
4	678	35
5	844	35
6	882	35
7	882	35
0	6	7
1	9	7
2	20	7
3	42	7
4	67	7
5	95	7
6	165	7
7	264	7
8	410	7
9	465	7
10	499	7
0	499	7

Iter	Nodes	Cost
0	6	18
1	9	18
2	20	18
3	42	18
4	67	18
5	95	18
6	165	18
7	264	18
8	410	18
9	465	18
10	499	18
0	499	18

Iter	Nodes	Cost
0	13	49
1	31	49
2	45	49
3	68	49
4	96	49
5	166	49
6	262	49
7	406	49
8	462	49
9	494	49
0	494	49

analyze0.0ms (0%)

sample532.0ms (10.6%)

preprocess47.0ms (0.9%)

explain79.0ms (1.6%)

eval0.0ms (0%)

prune32.0ms (0.6%)

simplify18.0ms (0.4%)

localize20.0ms (0.4%)

series3.0ms (0.1%)

rewrite544.0ms (10.8%)

simplify179.0ms (3.6%)

eval37.0ms (0.7%)

prune36.0ms (0.7%)

simplify30.0ms (0.6%)

localize62.0ms (1.2%)

series5.0ms (0.1%)

rewrite449.0ms (8.9%)

simplify258.0ms (5.1%)

eval69.0ms (1.4%)

prune48.0ms (0.9%)

simplify3.0ms (0.1%)

localize134.0ms (2.7%)

series1.0ms (0%)

rewrite681.0ms (13.5%)

simplify5.0ms (0.1%)

eval6.0ms (0.1%)

prune3.0ms (0.1%)

simplify3.0ms (0.1%)

localize14.0ms (0.3%)

series0.0ms (0%)

rewrite7.0ms (0.1%)

simplify3.0ms (0.1%)

eval1.0ms (0%)

prune5.0ms (0.1%)

regimes24.0ms (0.5%)

regimes20.0ms (0.4%)

regimes15.0ms (0.3%)

regimes14.0ms (0.3%)

regimes9.0ms (0.2%)

regimes11.0ms (0.2%)

regimes7.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

soundness1.6s (31.3%)

preprocess38.0ms (0.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	16	37
1	46	35
2	129	35
3	381	35
4	678	35
5	844	35
6	882	35
7	882	35
0	6	7
1	9	7
2	20	7
3	42	7
4	67	7
5	95	7
6	165	7
7	264	7
8	410	7
9	465	7
10	499	7
0	499	7

Iter	Nodes	Cost
0	6	18
1	9	18
2	20	18
3	42	18
4	67	18
5	95	18
6	165	18
7	264	18
8	410	18
9	465	18
10	499	18
0	499	18

Iter	Nodes	Cost
0	13	49
1	31	49
2	45	49
3	68	49
4	96	49
5	166	49
6	262	49
7	406	49
8	462	49
9	494	49
0	494	49