Metrics for Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1

analyze0.0ms (0%)

Memory

1.0MiB live, 1.0MiB 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 11 to 10 computations (9.1% saved)

sample1.2s (23%)

Memory

3.0MiB live, 1 120.8MiB allocated

Samples

851.0ms	8 253×	0	valid
0.0ms	2×	1	valid
0.0ms	1×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 444.0ms

ival-div: 291.0ms (65.6% of total)

ival-add: 86.0ms (19.4% of total)

ival-mult: 53.0ms (11.9% of total)

exact: 5.0ms (1.1% of total)

ival-true: 5.0ms (1.1% of total)

ival-assert: 3.0ms (0.7% of total)

adjust: 0.0ms (0% of total)

Bogosity

preprocess81.0ms (1.6%)

Memory

22.5MiB live, 61.3MiB allocated

Algorithm

2×	egg-herbie

Rules

412×	`distribute-rgt-in`
356×	`sub-neg`
278×	`unsub-neg`
242×	`cancel-sign-sub`
240×	`associate-+l-`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	97
1	92	91
2	238	90
3	668	76
4	1199	72
5	1787	70
6	2256	70
7	2444	70
8	2492	70
9	2500	70
10	2500	70
11	2500	70
0	8	9
1	13	9
2	20	9
3	22	9
0	22	8

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

Inputs
(+ (+ (/ x 2) (* y x)) z)
(+ (+ (/ (neg x) 2) (* y (neg x))) z)
(+ (+ (/ x 2) (* (neg y) x)) z)
(+ (+ (/ x 2) (* y x)) (neg z))
(neg (+ (+ (/ (neg x) 2) (* y (neg x))) z))
(neg (+ (+ (/ x 2) (* (neg y) x)) z))
(neg (+ (+ (/ x 2) (* y x)) (neg z)))
(+ (+ (/ y 2) (* x y)) z)
(+ (+ (/ z 2) (* y z)) x)
(+ (+ (/ x 2) (* z x)) y)

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

explain94.0ms (1.8%)

Memory

7.1MiB live, 244.1MiB allocated

FPErrors

Click to see full error table

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

31.0ms

512×

valid

Compiler

Compiled 80 to 36 computations (55% saved)

Precisions

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

ival-add: 5.0ms (39.6% of total)

ival-mult: 4.0ms (31.7% of total)

ival-div: 3.0ms (23.8% 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: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify8.0ms (0.2%)

Memory

-26.7MiB live, 15.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

24×	`+-lowering-+.f64`
24×	`+-lowering-+.f32`
12×	`accelerator-lowering-fma.f32`
12×	`accelerator-lowering-fma.f64`
10×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	13	26
2	20	26
3	22	26
0	22	24

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize24.0ms (0.5%)

Memory

22.4MiB live, 60.3MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

16.0ms

256×

valid

Compiler

Compiled 28 to 10 computations (64.3% saved)

Precisions

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

ival-div: 2.0ms (32.3% of total)

ival-add: 2.0ms (32.3% of total)

ival-mult: 2.0ms (32.3% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

11.8MiB live, 11.8MiB allocated

Counts

4 → 96

Calls

Call 1

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

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

Calls

24 calls:

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

rewrite363.0ms (6.9%)

Memory

-0.9MiB live, 591.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 074×	`accelerator-lowering-fma.f32`
7 074×	`accelerator-lowering-fma.f64`
4 356×	`-lowering-.f32`
4 356×	`-lowering-.f64`
2 578×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	48	18
2	448	18
3	6054	18
0	8017	17

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 242

Calls

Call 1

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

Outputs
(+.f64 (/.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 x y) z))
(+.f64 (*.f64 x y) (+.f64 (/.f64 x #s(literal 2 binary64)) z))
(+.f64 (*.f64 x (+.f64 y #s(literal 1/2 binary64))) z)
(+.f64 z (*.f64 x (+.f64 y #s(literal 1/2 binary64))))
(+.f64 (+.f64 (*.f64 x y) z) (/.f64 x #s(literal 2 binary64)))
(+.f64 (/.f64 (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (-.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) z))))
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) z) (*.f64 x y))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) z))) #s(literal -1 binary64)))
(-.f64 (+.f64 (*.f64 x y) z) (/.f64 x #s(literal -2 binary64)))
(-.f64 (.f64 (/.f64 (.f64 x x) x) (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) y))) (-.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) z))
(-.f64 (/.f64 (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (-.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) z)) (/.f64 (.f64 z z) (-.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) z)))
(-.f64 (/.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (-.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) z)) (/.f64 (.f64 (+.f64 (.f64 x y) z) (+.f64 (.f64 x y) z)) (-.f64 (*.f64 x (-.f64 #s(literal 1/2 binary64) y)) z)))
(-.f64 (/.f64 (.f64 z z) (-.f64 z (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (/.f64 (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (-.f64 z (.f64 x (+.f64 y #s(literal 1/2 binary64))))))
(-.f64 (+.f64 z (.f64 (/.f64 (.f64 x x) x) (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) y)))) (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y))))
(fma.f64 x y (+.f64 (/.f64 x #s(literal 2 binary64)) z))
(fma.f64 x #s(literal 1/2 binary64) (+.f64 (*.f64 x y) z))
(fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z)
(fma.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1 binary64) (+.f64 (*.f64 x y) z))
(fma.f64 y x (+.f64 (/.f64 x #s(literal 2 binary64)) z))
(fma.f64 (*.f64 x y) #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal 2 binary64)) z))
(fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 (*.f64 x (-.f64 #s(literal 1/2 binary64) y)) (/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1/2 binary64) y))) z)
(fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (/.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (-.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (*.f64 x (+.f64 y #s(literal 1/2 binary64))) z))))
(fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (/.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))) z)
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64) (+.f64 (*.f64 x y) z))
(fma.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64)))))) z)
(fma.f64 (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64))))) (.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64))))))) z)
(fma.f64 (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64))))) (/.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (*.f64 x (-.f64 y #s(literal 1/2 binary64)))))) z)
(fma.f64 (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) z))))
(fma.f64 #s(literal 1 binary64) (/.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 x y) z))
(fma.f64 #s(literal 1 binary64) (*.f64 x y) (+.f64 (/.f64 x #s(literal 2 binary64)) z))
(fma.f64 #s(literal 1 binary64) (*.f64 x (+.f64 y #s(literal 1/2 binary64))) z)
(fma.f64 #s(literal 1/2 binary64) x (+.f64 (*.f64 x y) z))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 x y) z))
(fma.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 y y))) (/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1/2 binary64) y)) z)
(fma.f64 #s(literal -1 binary64) (/.f64 x #s(literal -2 binary64)) (+.f64 (*.f64 x y) z))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64))))))) z)
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y)))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 1/2 binary64) y))) z)
(fma.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (.f64 z (.f64 z z))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 z (-.f64 z (.f64 x y))))) (/.f64 x #s(literal 2 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64)))))) (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) z)
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1/2 binary64) y)) (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 y y))) z)
(fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x) (+.f64 (*.f64 x y) z))
(fma.f64 (.f64 (.f64 x x) (-.f64 (.f64 y y) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (.f64 x (-.f64 y #s(literal 1/2 binary64)))) z)
(fma.f64 (-.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 z z)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x y) z)) (/.f64 x #s(literal 2 binary64)))
(fma.f64 (+.f64 y #s(literal 1/2 binary64)) x z)
(fma.f64 (/.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) x) (/.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) (-.f64 #s(literal 1/2 binary64) y)) z)
(fma.f64 (pow.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (+.f64 (*.f64 x y) z))
(fma.f64 (*.f64 #s(literal 1 binary64) y) x (+.f64 (/.f64 x #s(literal 2 binary64)) z))
(fma.f64 (/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y)))) (*.f64 x (+.f64 y #s(literal 1/2 binary64))) z)
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(fma.f64 (pow.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 x y))
(fma.f64 (*.f64 #s(literal 1 binary64) y) x (/.f64 x #s(literal 2 binary64)))
(fma.f64 (/.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y)))) (.f64 x (+.f64 y #s(literal 1/2 binary64))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))))
(fma.f64 (/.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y))))) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 y #s(literal 1/2 binary64)))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 y #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 y #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (-.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 y y) #s(literal 1/4 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 y #s(literal 1/2 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y)))) (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 1/2 binary64) y)))
(/.f64 (+.f64 (.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (.f64 (.f64 x y) (.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))))))) (.f64 (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64))))) (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (/.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64)))))))
(/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y))))) (.f64 (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y))))))
(/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y))))) (.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/16 binary64)) (.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 y y)))))))
(/.f64 (.f64 (.f64 x x) (-.f64 (.f64 y y) #s(literal 1/4 binary64))) (.f64 x (-.f64 y #s(literal 1/2 binary64))))
(/.f64 (.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y)))) (.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 y y)))))
(/.f64 (-.f64 (.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) (.f64 x (.f64 x (.f64 y y))))) (.f64 x (.f64 (-.f64 #s(literal 1/2 binary64) y) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y))))) (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 1/2 binary64) y))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (-.f64 (.f64 y y) #s(literal 1/4 binary64)))) (neg.f64 (.f64 x (-.f64 y #s(literal 1/2 binary64)))))
(/.f64 (/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 y y))) x) (-.f64 #s(literal 1/2 binary64) y))
(/.f64 (-.f64 (pow.f64 (.f64 (/.f64 (.f64 x x) x) (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) y))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (/.f64 (.f64 x x) x) (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) y))) (.f64 (/.f64 (.f64 x x) x) (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) y)))) (+.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))) (.f64 (.f64 (/.f64 (.f64 x x) x) (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) y))) (/.f64 (.f64 x (.f64 x (.f64 y y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))))))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 (.f64 x x) x) (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) y))) (.f64 (/.f64 (.f64 x x) x) (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) y)))) (.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y))))) (+.f64 (.f64 (/.f64 (.f64 x x) x) (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) y))) (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))))
(/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64)) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (*.f64 x (-.f64 y #s(literal 1/2 binary64))))))
(/.f64 (.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y))) #s(literal 1 binary64)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))
(/.f64 (.f64 (+.f64 (.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (.f64 (.f64 x y) (.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))))))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64))))))) (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (/.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64))))))
(/.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y))))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64))))))) (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y)))))
(/.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y))))) (/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1/2 binary64) y))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/16 binary64)) (.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (*.f64 y y))))))
(/.f64 (.f64 (.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y)))) (/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1/2 binary64) y))) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (*.f64 y y))))
(pow.f64 (*.f64 x (+.f64 y #s(literal 1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 y #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 y #s(literal 1/2 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 x (-.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 y y) #s(literal 1/4 binary64)))) #s(literal -1 binary64))
(*.f64 x (+.f64 y #s(literal 1/2 binary64)))
(.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) (/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1/2 binary64) y))))
(.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (/.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) (.f64 x (-.f64 #s(literal 1/2 binary64) y))))
(.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (*.f64 x (-.f64 y #s(literal 1/2 binary64)))))))
(.f64 (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64))))) (.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (*.f64 x (-.f64 y #s(literal 1/2 binary64))))))))
(.f64 (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64))))) (/.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64)))))))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 y #s(literal 1/2 binary64))))
(.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y))) (/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1/2 binary64) y)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (*.f64 x (-.f64 y #s(literal 1/2 binary64))))))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y)))) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 1/2 binary64) y))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64)))))) (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 y (*.f64 y y)) #s(literal 1/8 binary64))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1/2 binary64) y)) (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y))))
(.f64 (.f64 (.f64 x x) (-.f64 (.f64 y y) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x (-.f64 y #s(literal 1/2 binary64)))))
(*.f64 (+.f64 y #s(literal 1/2 binary64)) x)
(.f64 (/.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) x) (/.f64 (*.f64 x (-.f64 #s(literal 1/2 binary64) y)) (-.f64 #s(literal 1/2 binary64) y)))
(.f64 (/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y)))) (.f64 x (+.f64 y #s(literal 1/2 binary64))))
(.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64)) (.f64 (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64)))) (.f64 (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64)))) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64)))))))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/16 binary64)) (.f64 (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64)))) (-.f64 (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64)))) (/.f64 x (/.f64 #s(literal 4 binary64) x))))))
(.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/16 binary64)) (.f64 (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64)))) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64))))))) (-.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (-.f64 y #s(literal 1/2 binary64))))))
(.f64 (/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y))))) (+.f64 (/.f64 x (/.f64 #s(literal 4 binary64) x)) (.f64 (.f64 x y) (.f64 x (+.f64 y #s(literal 1/2 binary64))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 x #s(literal -2 binary64)))
(neg.f64 (/.f64 x #s(literal -2 binary64)))
(neg.f64 (*.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))
(/.f64 x #s(literal 2 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(pow.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 x #s(literal 2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal -1 binary64) (/.f64 x #s(literal -2 binary64)))
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x))
(*.f64 (pow.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 x y)
(*.f64 y x)
(.f64 (.f64 x y) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x y))
(.f64 (.f64 #s(literal 1 binary64) y) x)

simplify216.0ms (4.1%)

Memory

-9.8MiB live, 312.5MiB allocated

Algorithm

1×	egg-herbie

Rules

6 434×	`accelerator-lowering-fma.f32`
6 434×	`accelerator-lowering-fma.f64`
2 474×	`-lowering-.f32`
2 474×	`-lowering-.f64`
1 356×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	440
1	174	440
2	488	440
3	1318	440
4	3632	440
5	6705	440
0	8250	412

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

eval37.0ms (0.7%)

Memory: -7.9MiB live, 67.5MiB allocated
Compiler: Compiled 8 223 to 760 computations (90.8% saved)

prune37.0ms (0.7%)

Memory

-7.7MiB live, 72.5MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	333	5	338
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	333	6	339

Accuracy

100.0%

Counts

339 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
▶	78.3%	(+.f64 (*.f64 x y) z)
▶	63.4%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
▶	60.3%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
▶	39.0%	(*.f64 x y)
▶	41.7%	z

Compiler

Compiled 80 to 56 computations (30% saved)

simplify5.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Rules

16×	`+-lowering-+.f64`
16×	`+-lowering-+.f32`
16×	`accelerator-lowering-fma.f32`
16×	`accelerator-lowering-fma.f64`
12×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	18	39
2	19	39
0	19	37

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize32.0ms (0.6%)

Memory

11.7MiB live, 49.7MiB allocated

Localize:

Found 7 expressions of interest:

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

Samples

20.0ms

256×

valid

Compiler

Compiled 41 to 12 computations (70.7% saved)

Precisions

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

ival-mult: 5.0ms (57.5% of total)

ival-add: 4.0ms (46% 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

6.0MiB live, 6.0MiB allocated

Counts

6 → 132

Calls

Call 1

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

Outputs
#<alt z>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt (* x y)>
#<alt (* x (+ y (/ z x)))>
#<alt (* x (+ y (/ z x)))>
#<alt (* x (+ y (/ z x)))>
#<alt (* x y)>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))>
#<alt z>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt (* x y)>
#<alt (* y (+ x (/ z y)))>
#<alt (* y (+ x (/ z y)))>
#<alt (* y (+ x (/ z y)))>
#<alt (* x y)>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))>
#<alt (* x y)>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt z>
#<alt (* z (+ 1 (/ (* x y) z)))>
#<alt (* z (+ 1 (/ (* x y) z)))>
#<alt (* z (+ 1 (/ (* x y) z)))>
#<alt z>
#<alt (* -1 (* z (- (* -1 (/ (* x y) z)) 1)))>
#<alt (* -1 (* z (- (* -1 (/ (* x y) z)) 1)))>
#<alt (* -1 (* z (- (* -1 (/ (* x y) z)) 1)))>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* 1/2 x)>
#<alt (+ (* 1/2 x) (* x y))>
#<alt (+ (* 1/2 x) (* x y))>
#<alt (+ (* 1/2 x) (* x y))>
#<alt (* x y)>
#<alt (* y (+ x (* 1/2 (/ x y))))>
#<alt (* y (+ x (* 1/2 (/ x y))))>
#<alt (* y (+ x (* 1/2 (/ x y))))>
#<alt (* x y)>
#<alt (* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))>
#<alt 1/2>
#<alt (+ 1/2 y)>
#<alt (+ 1/2 y)>
#<alt (+ 1/2 y)>
#<alt y>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt y>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt z>
#<alt (+ z (* 1/2 x))>
#<alt (+ z (* 1/2 x))>
#<alt (+ z (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ z x)))>
#<alt (* x (+ 1/2 (/ z x)))>
#<alt (* x (+ 1/2 (/ z x)))>
#<alt (* 1/2 x)>
#<alt (* -1 (* x (- (* -1 (/ z x)) 1/2)))>
#<alt (* -1 (* x (- (* -1 (/ z x)) 1/2)))>
#<alt (* -1 (* x (- (* -1 (/ z x)) 1/2)))>
#<alt (* 1/2 x)>
#<alt (+ z (* 1/2 x))>
#<alt (+ z (* 1/2 x))>
#<alt (+ z (* 1/2 x))>
#<alt z>
#<alt (* z (+ 1 (* 1/2 (/ x z))))>
#<alt (* z (+ 1 (* 1/2 (/ x z))))>
#<alt (* z (+ 1 (* 1/2 (/ x z))))>
#<alt z>
#<alt (* -1 (* z (- (* -1/2 (/ x z)) 1)))>
#<alt (* -1 (* z (- (* -1/2 (/ x z)) 1)))>
#<alt (* -1 (* z (- (* -1/2 (/ x z)) 1)))>
#<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
0.0ms	x	@	0	(* x (+ 1/2 y))
0.0ms	x	@	inf	(* x (+ 1/2 y))
0.0ms	y	@	inf	(* x (+ 1/2 y))
0.0ms	x	@	-inf	(* x (+ 1/2 y))
0.0ms	y	@	-inf	(* x (+ 1/2 y))

rewrite461.0ms (8.8%)

Memory

-21.5MiB live, 578.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 658×	`accelerator-lowering-fma.f32`
6 658×	`accelerator-lowering-fma.f64`
5 056×	`-lowering-.f32`
5 056×	`-lowering-.f64`
4 140×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	55	24
2	406	24
3	4014	24
0	9583	22

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 412

Calls

Call 1

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

Outputs
(+.f64 (*.f64 x y) z)
(+.f64 z (*.f64 x y))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (.f64 x y) z))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x y) z))) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (/.f64 (.f64 z z) (-.f64 (.f64 x y) z)))
(-.f64 (/.f64 (.f64 z z) (-.f64 z (.f64 x y))) (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 z (.f64 x y))))
(fma.f64 x y z)
(fma.f64 x (/.f64 (.f64 x (.f64 y y)) (-.f64 (.f64 x y) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (*.f64 x y) z))))
(fma.f64 y x z)
(fma.f64 y (/.f64 (.f64 x (.f64 x y)) (-.f64 (.f64 x y) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (*.f64 x y) z))))
(fma.f64 y (pow.f64 x #s(literal 1 binary64)) z)
(fma.f64 y (exp.f64 (log.f64 x)) z)
(fma.f64 (.f64 x y) (/.f64 (.f64 x y) (-.f64 (.f64 x y) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (*.f64 x y) z))))
(fma.f64 (.f64 x (.f64 x (.f64 y y))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x y) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (.f64 x y) z))))
(fma.f64 (.f64 y y) (/.f64 (.f64 x x) (-.f64 (.f64 x y) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (*.f64 x y) z))))
(fma.f64 (.f64 x x) (/.f64 (.f64 y y) (-.f64 (.f64 x y) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (*.f64 x y) z))))
(fma.f64 (.f64 x (.f64 y y)) (/.f64 x (-.f64 (.f64 x y) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (*.f64 x y) z))))
(fma.f64 (.f64 x (.f64 x y)) (/.f64 y (-.f64 (.f64 x y) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (*.f64 x y) z))))
(fma.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 z z))) (+.f64 (.f64 x y) z) (neg.f64 (/.f64 (.f64 z z) (-.f64 (.f64 x y) z))))
(fma.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z)))) (+.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 z (+.f64 (.f64 x y) z))) (neg.f64 (/.f64 (.f64 z z) (-.f64 (*.f64 x y) z))))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) y z)
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(.f64 (/.f64 (+.f64 (.f64 z (.f64 z z)) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 z (+.f64 z (.f64 x #s(literal -1/2 binary64)))) (.f64 z (+.f64 z (.f64 x #s(literal -1/2 binary64))))))) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 z (+.f64 z (*.f64 x #s(literal -1/2 binary64))))))
(.f64 (/.f64 (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 z z)) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 z (.f64 z z)))) (+.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 z (+.f64 z (*.f64 x #s(literal 1/2 binary64))))))
(.f64 (pow.f64 (/.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) z) (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 z (.f64 (.f64 z (.f64 z z)) (.f64 z z))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 z z) (+.f64 (.f64 z z) (.f64 x (.f64 x #s(literal 1/4 binary64))))))))
(.f64 (pow.f64 (/.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) z) (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 z (.f64 z (.f64 z z))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 z z) (.f64 x (.f64 x #s(literal 1/4 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) z))) (+.f64 (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 (.f64 z (.f64 z z)) (.f64 z z)))) (.f64 #s(literal 1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 z (.f64 z z)) (-.f64 (.f64 z (.f64 z z)) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) z))) (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 z (.f64 (.f64 z (.f64 z z)) (.f64 z z))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 z (*.f64 z z)))))
(exp.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 #s(literal 1/2 binary64))))
(*.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) (exp.f64 (log.f64 x)))

simplify276.0ms (5.3%)

Memory

17.5MiB live, 339.5MiB allocated

Algorithm

1×	egg-herbie

Rules

5 686×	`accelerator-lowering-fma.f32`
5 686×	`accelerator-lowering-fma.f64`
3 028×	`-lowering-.f32`
3 028×	`-lowering-.f64`
1 240×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	508
1	200	508
2	512	508
3	1440	508
4	3343	508
5	5374	508
6	7166	508
7	7996	508
0	8046	463

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

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

eval82.0ms (1.6%)

Memory: 24.9MiB live, 137.1MiB allocated
Compiler: Compiled 13 137 to 1 240 computations (90.6% saved)

prune147.0ms (2.8%)

Memory

-23.2MiB live, 127.7MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	575	2	577
Fresh	0	0	0
Picked	0	5	5
Done	1	0	1
Total	576	7	583

Accuracy

100.0%

Counts

583 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.3%	(+.f64 (.f64 x y) (.f64 x #s(literal 1/2 binary64)))
✓	78.3%	(+.f64 (*.f64 x y) z)
✓	63.4%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
✓	60.3%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	39.0%	(*.f64 x y)
▶	23.9%	(*.f64 x #s(literal 1/2 binary64))
✓	41.7%	z

Compiler

Compiled 50 to 36 computations (28% saved)

simplify4.0ms (0.1%)

Memory

10.2MiB live, 10.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

12×	`-lowering-.f32`
12×	`-lowering-.f64`
8×	`+-lowering-+.f64`
8×	`+-lowering-+.f32`
8×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
1	11	19
2	14	19
0	14	19

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize26.0ms (0.5%)

Memory

-1.0MiB live, 45.1MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

17.0ms

256×

valid

Compiler

Compiled 23 to 9 computations (60.9% saved)

Precisions

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

ival-mult: 4.0ms (75.3% of total)

ival-add: 1.0ms (18.8% 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

2.3MiB live, 2.3MiB allocated

Counts

3 → 60

Calls

Call 1

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

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

Calls

15 calls:

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

rewrite533.0ms (10.2%)

Memory

-6.0MiB live, 751.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

10 244×	`accelerator-lowering-fma.f32`
10 244×	`accelerator-lowering-fma.f64`
4 484×	`/-lowering-/.f32`
4 484×	`/-lowering-/.f64`
4 384×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	24	11
2	191	11
3	1992	11
0	8180	11

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 220

Calls

Call 1

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

Outputs
(exp.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 #s(literal 1/2 binary64))))
(*.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) (exp.f64 (log.f64 x)))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x y))
(+.f64 (.f64 x y) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (.f64 (/.f64 (.f64 x (.f64 x y)) x) (/.f64 y (+.f64 y #s(literal -1/2 binary64)))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) y)))) #s(literal -1 binary64)))
(-.f64 (.f64 (/.f64 (.f64 x (.f64 x y)) x) (/.f64 y (+.f64 y #s(literal -1/2 binary64)))) (.f64 (/.f64 x x) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (/.f64 (.f64 x (.f64 x (.f64 y y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 y #s(literal -1/2 binary64)))) (/.f64 (.f64 (.f64 x x) (+.f64 (.f64 y y) #s(literal -1/4 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 y #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y))))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))) (+.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x y) (.f64 x (+.f64 y #s(literal -1/2 binary64)))))) (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))) (+.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x y) (*.f64 x (+.f64 y #s(literal -1/2 binary64)))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y))))) (+.f64 (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y))))) (.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 y y) #s(literal 1/4 binary64)))))) (.f64 x (+.f64 y #s(literal -1/2 binary64)))) (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))) (+.f64 (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y))))) (.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 y y) #s(literal 1/4 binary64)))))) (*.f64 x (+.f64 y #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y))))) (.f64 (.f64 x x) (+.f64 (.f64 y y) #s(literal 1/4 binary64)))) (.f64 x (+.f64 y #s(literal -1/2 binary64)))) (/.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (+.f64 (.f64 y y) #s(literal 1/4 binary64)))) (*.f64 x (+.f64 y #s(literal -1/2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x y) (.f64 x (+.f64 y #s(literal -1/2 binary64))))))) (/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y)))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x y) (*.f64 x (+.f64 y #s(literal -1/2 binary64))))))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y))))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x y) (.f64 x (+.f64 y #s(literal -1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))))) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x y) (.f64 x (+.f64 y #s(literal -1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 y (*.f64 y y)) #s(literal 1/8 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y))))) (.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (+.f64 (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y))))) (.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 y y) #s(literal 1/4 binary64))))))) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))) (.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (+.f64 (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y))))) (.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x x) (+.f64 (*.f64 y y) #s(literal 1/4 binary64))))))))
(-.f64 (/.f64 (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y))))) (.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 y y) #s(literal 1/4 binary64))))) (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (.f64 (.f64 x x) (+.f64 (*.f64 y y) #s(literal 1/4 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (+.f64 y #s(literal -1/2 binary64)))) (.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (.f64 x (+.f64 y #s(literal -1/2 binary64))))) (/.f64 (.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (.f64 x (.f64 x #s(literal 1/4 binary64)))) (.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (*.f64 x (+.f64 y #s(literal -1/2 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 (/.f64 (.f64 x (.f64 x y)) x) (/.f64 y (+.f64 y #s(literal -1/2 binary64)))) (/.f64 (.f64 (/.f64 (.f64 x (.f64 x y)) x) (/.f64 y (+.f64 y #s(literal -1/2 binary64)))) (/.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 y y)))))) (+.f64 (/.f64 (.f64 (/.f64 (.f64 x (.f64 x y)) x) (/.f64 y (+.f64 y #s(literal -1/2 binary64)))) (/.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 y y))))) (+.f64 (/.f64 (.f64 (/.f64 x x) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64)))) (/.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (/.f64 (.f64 (/.f64 (.f64 x (.f64 x y)) x) (/.f64 y (+.f64 y #s(literal -1/2 binary64)))) (/.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (.f64 x (.f64 x #s(literal 1/4 binary64)))))))) (/.f64 (.f64 (.f64 (/.f64 x x) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64)))) (/.f64 (.f64 (/.f64 x x) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64)))) (/.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (.f64 x (.f64 x #s(literal 1/4 binary64)))))) (+.f64 (/.f64 (.f64 (/.f64 (.f64 x (.f64 x y)) x) (/.f64 y (+.f64 y #s(literal -1/2 binary64)))) (/.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 y y))))) (+.f64 (/.f64 (.f64 (/.f64 x x) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64)))) (/.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (/.f64 (.f64 (/.f64 (.f64 x (.f64 x y)) x) (/.f64 y (+.f64 y #s(literal -1/2 binary64)))) (/.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (.f64 x (*.f64 x #s(literal 1/4 binary64)))))))))
(-.f64 (/.f64 (/.f64 (.f64 (/.f64 (.f64 x (.f64 x y)) x) (/.f64 y (+.f64 y #s(literal -1/2 binary64)))) (/.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 y y))))) (+.f64 (.f64 (/.f64 (.f64 x (.f64 x y)) x) (/.f64 y (+.f64 y #s(literal -1/2 binary64)))) (.f64 (/.f64 x x) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64)))))) (/.f64 (/.f64 (.f64 (/.f64 x x) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64)))) (/.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (+.f64 (.f64 (/.f64 (.f64 x (.f64 x y)) x) (/.f64 y (+.f64 y #s(literal -1/2 binary64)))) (.f64 (/.f64 x x) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64)))))))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 x y))
(fma.f64 x y (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 x (/.f64 (.f64 x (.f64 y y)) (.f64 x (+.f64 y #s(literal -1/2 binary64)))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 x y))
(fma.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 1 binary64)) (*.f64 x y))
(fma.f64 y x (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 y (/.f64 (.f64 x (.f64 x y)) (.f64 x (+.f64 y #s(literal -1/2 binary64)))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (.f64 x y) (/.f64 (.f64 x y) (.f64 x (+.f64 y #s(literal -1/2 binary64)))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (.f64 x (.f64 x (.f64 y y))) (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 y #s(literal -1/2 binary64))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (.f64 y y) (/.f64 (.f64 x x) (.f64 x (+.f64 y #s(literal -1/2 binary64)))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 x (.f64 x y)) x) (/.f64 y (+.f64 y #s(literal -1/2 binary64)))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 x (+.f64 y #s(literal -1/2 binary64)))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (.f64 x (.f64 x y)) (/.f64 y (.f64 x (+.f64 y #s(literal -1/2 binary64)))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (.f64 x (.f64 y y)) (/.f64 x (.f64 x (+.f64 y #s(literal -1/2 binary64)))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (neg.f64 (.f64 x (.f64 x (.f64 y y)))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 y #s(literal -1/2 binary64)))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 x x) (/.f64 (.f64 x (.f64 y y)) (+.f64 y #s(literal -1/2 binary64))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 y x) (/.f64 (.f64 x (.f64 x y)) (+.f64 y #s(literal -1/2 binary64))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 x y) x) (/.f64 (.f64 x y) (+.f64 y #s(literal -1/2 binary64))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 y y) x) (/.f64 (.f64 x x) (+.f64 y #s(literal -1/2 binary64))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 x x) x) (/.f64 (.f64 y y) (+.f64 y #s(literal -1/2 binary64))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 x (.f64 x y)) x) (/.f64 y (+.f64 y #s(literal -1/2 binary64))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 x (.f64 y y)) x) (/.f64 x (+.f64 y #s(literal -1/2 binary64))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) x) (/.f64 #s(literal 1 binary64) (+.f64 y #s(literal -1/2 binary64))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 (.f64 x x) (+.f64 (.f64 y y) #s(literal -1/4 binary64)))) (.f64 x (+.f64 #s(literal 1/2 binary64) y)) (neg.f64 (.f64 (/.f64 x x) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))) (+.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) y)))) (neg.f64 (.f64 (/.f64 x x) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64) (*.f64 x y))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 y #s(literal 1 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (pow.f64 y #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 x)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 y)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 #s(literal 1/2 binary64))) (*.f64 x y))
(fma.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) (exp.f64 (log.f64 x)) (*.f64 x y))
(neg.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y)))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x y) (.f64 x (+.f64 y #s(literal -1/2 binary64))))))))
(neg.f64 (/.f64 (.f64 (.f64 x x) (+.f64 (.f64 y y) #s(literal -1/4 binary64))) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 y #s(literal -1/2 binary64)))))
(neg.f64 (-.f64 (/.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x y) (.f64 x (+.f64 y #s(literal -1/2 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) y))))
(neg.f64 (-.f64 (/.f64 #s(literal 0 binary64) (.f64 x (+.f64 y #s(literal -1/2 binary64)))) (.f64 x (+.f64 #s(literal 1/2 binary64) y))))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) y)))
(/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y)))) (+.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x y) (.f64 x (+.f64 y #s(literal -1/2 binary64))))))
(/.f64 (.f64 (.f64 x x) (+.f64 (.f64 y y) #s(literal -1/4 binary64))) (.f64 x (+.f64 y #s(literal -1/2 binary64))))
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(.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y)))) (+.f64 (.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y))))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) (.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) (.f64 x (-.f64 #s(literal 1/2 binary64) y))))))) (+.f64 (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y))))) (.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (-.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (.f64 x (.f64 x (*.f64 y y)))))))
(.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y)))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x y) (.f64 x (+.f64 y #s(literal -1/2 binary64))))) (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 y y) #s(literal -1/4 binary64))) (.f64 (.f64 x (.f64 x y)) #s(literal -1/2 binary64))))) (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 y y) #s(literal -1/4 binary64))) (.f64 (.f64 x (.f64 x y)) #s(literal -1/2 binary64))))
(.f64 (/.f64 (.f64 (.f64 x x) (+.f64 (.f64 y y) #s(literal -1/4 binary64))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))) (+.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 (.f64 x #s(literal 1/2 binary64)) (*.f64 x (+.f64 #s(literal 1/2 binary64) y)))))
(.f64 (pow.f64 (/.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) y))) #s(literal -1 binary64)) (pow.f64 (/.f64 (+.f64 y #s(literal -1/2 binary64)) (*.f64 x (+.f64 y #s(literal -1/2 binary64)))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y))))) (.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 y y) #s(literal 1/4 binary64)))))))
(.f64 (pow.f64 (/.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (.f64 (.f64 (.f64 x x) (+.f64 (.f64 y y) #s(literal 1/4 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 y y) #s(literal -1/4 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 y y) #s(literal 1/4 binary64)))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x y) (.f64 x (+.f64 y #s(literal -1/2 binary64))))) (+.f64 (.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/512 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y))))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 x y) (.f64 x (.f64 x (*.f64 y y)))))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x y) (.f64 x (+.f64 y #s(literal -1/2 binary64))))) (.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))))
(exp.f64 (log.f64 (*.f64 x y)))
(exp.f64 (.f64 (log.f64 (.f64 x y)) #s(literal 1 binary64)))
(pow.f64 (*.f64 x y) #s(literal 1 binary64))
(*.f64 x y)
(*.f64 y x)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 y #s(literal 1 binary64)))
(*.f64 (pow.f64 y #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 y)))

simplify312.0ms (5.9%)

Memory

-1.0MiB live, 283.2MiB allocated

Algorithm

1×	egg-herbie

Rules

3 344×	`accelerator-lowering-fma.f32`
3 344×	`accelerator-lowering-fma.f64`
2 256×	`-lowering-.f32`
2 256×	`-lowering-.f64`
1 200×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	222
1	63	222
2	156	222
3	321	222
4	641	222
5	2249	222
6	3482	222
7	4059	222
8	4334	222
9	4365	222
10	4367	222
11	5220	222
12	6340	222
13	6764	222
14	7044	222
15	7094	222
16	7094	222
17	7666	222
18	7828	222
19	7984	222
0	8012	222

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

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

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

eval35.0ms (0.7%)

Memory: 12.9MiB live, 89.5MiB allocated
Compiler: Compiled 9 724 to 633 computations (93.5% saved)

prune117.0ms (2.2%)

Memory

-18.0MiB live, 98.2MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	301	0	301
Fresh	0	0	0
Picked	0	2	2
Done	0	5	5
Total	301	7	308

Accuracy

100.0%

Counts

308 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	60.3%	(+.f64 (.f64 x y) (.f64 x #s(literal 1/2 binary64)))
✓	78.3%	(+.f64 (*.f64 x y) z)
✓	63.4%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
✓	60.3%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	39.0%	(*.f64 x y)
✓	23.9%	(*.f64 x #s(literal 1/2 binary64))
✓	41.7%	z

Compiler

Compiled 91 to 52 computations (42.9% saved)

regimes20.0ms (0.4%)

Memory

3.8MiB live, 48.5MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

5 calls:

5.0ms	y
3.0ms	x
3.0ms	z
3.0ms	(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
3.0ms	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)

Results

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

Compiler

Compiled 34 to 24 computations (29.4% saved)

regimes10.0ms (0.2%)

Memory

18.2MiB live, 18.2MiB allocated

Counts

7 → 3

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	z
3.0ms	x
3.0ms	y

Results

Accuracy	Segments	Branch
89.7%	3	`x`
99.5%	3	`y`
88.3%	3	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes75.0ms (1.4%)

Memory

-20.8MiB live, 18.7MiB allocated

Counts

5 → 3

Calls

Call 1

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

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

Calls

3 calls:

69.0ms	x
3.0ms	z
3.0ms	y

Results

Accuracy	Segments	Branch
83.1%	3	`z`
85.4%	3	`x`
85.3%	3	`y`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes7.0ms (0.1%)

Memory

16.6MiB live, 16.6MiB allocated

Counts

4 → 3

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	z
2.0ms	x
2.0ms	y

Results

Accuracy	Segments	Branch
77.4%	3	`z`
66.1%	3	`y`
81.9%	3	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes32.0ms (0.6%)

Memory

-23.5MiB live, 13.9MiB allocated

Counts

3 → 3

Calls

Call 1

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

Outputs
(*.f64 x y)
z
(*.f64 x y)

Calls

3 calls:

2.0ms	z
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
63.7%	3	`y`
61.7%	3	`z`
64.0%	3	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes5.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated

Counts

2 → 3

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	z
2.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
51.4%	3	`z`
41.7%	1	`y`
53.5%	3	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes4.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
z

Outputs
z

Calls

3 calls:

1.0ms	y
1.0ms	x
1.0ms	z

Results

Accuracy	Segments	Branch
41.7%	1	`y`
41.7%	1	`z`
41.7%	1	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch34.0ms (0.6%)

Memory

-10.0MiB live, 69.6MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
16.0ms	1.637980309270954e-12	3.10129461492068e+20
15.0ms	-1.2579083694075003e+31	-3.723794277122214e-7

Samples

20.0ms

352×

valid

Compiler

Compiled 411 to 300 computations (27% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-div: 5.0ms (46.6% of total)

ival-add: 3.0ms (27.9% of total)

ival-mult: 2.0ms (18.6% of total)

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

exact: 0.0ms (0% of total)

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

bsearch22.0ms (0.4%)

Memory

-1.8MiB live, 37.5MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
9.0ms	2.5681301391947786e-69	2.16823674208642e-68
11.0ms	-1.052127190799832e+23	-45897705976710.53

Samples

12.0ms

240×

valid

Compiler

Compiled 285 to 224 computations (21.4% saved)

Precisions

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

ival-div: 2.0ms (36.2% of total)

ival-add: 2.0ms (36.2% of total)

ival-mult: 2.0ms (36.2% of total)

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

exact: 0.0ms (0% of total)

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

bsearch22.0ms (0.4%)

Memory

6.4MiB live, 45.1MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
9.0ms	2.5681301391947786e-69	2.16823674208642e-68
11.0ms	-6.7808216432831245e-84	-5.1276991275847244e-92

Samples

11.0ms

240×

valid

Compiler

Compiled 225 to 179 computations (20.4% saved)

Precisions

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

ival-div: 2.0ms (35.2% of total)

ival-add: 2.0ms (35.2% of total)

ival-mult: 2.0ms (35.2% of total)

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

exact: 0.0ms (0% of total)

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

bsearch28.0ms (0.5%)

Memory

26.8MiB live, 64.4MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
12.0ms	4.3199142869794396e-63	2.545503611105982e-53
13.0ms	-1.052127190799832e+23	-45897705976710.53

Samples

16.0ms

304×

valid

Compiler

Compiled 243 to 185 computations (23.9% saved)

Precisions

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

ival-add: 3.0ms (42.4% of total)

ival-div: 2.0ms (28.2% of total)

ival-mult: 2.0ms (28.2% of total)

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

exact: 0.0ms (0% of total)

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

bsearch36.0ms (0.7%)

Memory

-47.7MiB live, 63.0MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	3.258663528491464e+37	4.0039413241741615e+43
20.0ms	-6.271437590607268e+25	-1.052127190799832e+23

Samples

15.0ms

272×

valid

Compiler

Compiled 219 to 184 computations (16% saved)

Precisions

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

ival-div: 2.0ms (31.1% of total)

ival-add: 2.0ms (31.1% of total)

ival-mult: 2.0ms (31.1% of total)

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

exact: 0.0ms (0% of total)

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

simplify25.0ms (0.5%)

Memory

-10.5MiB live, 26.4MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
10×	`if-if-or-not_binary32`
6×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	89
1	68	89

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(if (<=.f64 y #s(literal -1/2 binary64)) (+.f64 (.f64 x y) z) (if (<=.f64 y #s(literal 1/2 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) z) (+.f64 (*.f64 x y) z)))
(if (<=.f64 x #s(literal -850000000000000000000 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 x #s(literal 6313673899733619/485667223056432267729865476705879726660601709763034880312953102434726071301302124544 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) z) (*.f64 x (+.f64 #s(literal 1/2 binary64) y))))
(if (<=.f64 x #s(literal -1063878752534457/279968092772225526319680285071055534765205687154331191862498637620473983897520118172609686658950889472 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 x #s(literal 4468138452119177/971334446112864535459730953411759453321203419526069760625906204869452142602604249088 binary64)) z (.f64 x (+.f64 #s(literal 1/2 binary64) y))))
(if (<=.f64 x #s(literal -65000000000000 binary64)) (.f64 x y) (if (<=.f64 x #s(literal 6875155298465649/904625697166532776746648320380374280103671755200316906558262375061821325312 binary64)) z (.f64 x y)))
(if (<=.f64 x #s(literal -4750000000000000054525952 binary64)) (.f64 x #s(literal 1/2 binary64)) (if (<=.f64 x #s(literal 6000000000000000578799285889800569438076928 binary64)) z (.f64 x #s(literal 1/2 binary64))))
z

Outputs
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 x y)) z)
(if (<=.f64 y #s(literal -1/2 binary64)) (+.f64 (.f64 x y) z) (if (<=.f64 y #s(literal 1/2 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) z) (+.f64 (*.f64 x y) z)))
(if (<=.f64 y #s(literal -1/2 binary64)) (+.f64 z (.f64 x y)) (if (<=.f64 y #s(literal 1/2 binary64)) (+.f64 z (.f64 x #s(literal 1/2 binary64))) (+.f64 z (*.f64 x y))))
(if (<=.f64 x #s(literal -850000000000000000000 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 x #s(literal 6313673899733619/485667223056432267729865476705879726660601709763034880312953102434726071301302124544 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) z) (*.f64 x (+.f64 #s(literal 1/2 binary64) y))))
(if (<=.f64 x #s(literal -850000000000000000000 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))) (if (<=.f64 x #s(literal 6313673899733619/485667223056432267729865476705879726660601709763034880312953102434726071301302124544 binary64)) (+.f64 z (.f64 x #s(literal 1/2 binary64))) (*.f64 x (+.f64 y #s(literal 1/2 binary64)))))
(if (<=.f64 x #s(literal -1063878752534457/279968092772225526319680285071055534765205687154331191862498637620473983897520118172609686658950889472 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 x #s(literal 4468138452119177/971334446112864535459730953411759453321203419526069760625906204869452142602604249088 binary64)) z (.f64 x (+.f64 #s(literal 1/2 binary64) y))))
(if (<=.f64 x #s(literal -1063878752534457/279968092772225526319680285071055534765205687154331191862498637620473983897520118172609686658950889472 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))) (if (<=.f64 x #s(literal 4468138452119177/971334446112864535459730953411759453321203419526069760625906204869452142602604249088 binary64)) z (.f64 x (+.f64 y #s(literal 1/2 binary64)))))
(if (<=.f64 x #s(literal -65000000000000 binary64)) (.f64 x y) (if (<=.f64 x #s(literal 6875155298465649/904625697166532776746648320380374280103671755200316906558262375061821325312 binary64)) z (.f64 x y)))
(if (<=.f64 x #s(literal -4750000000000000054525952 binary64)) (.f64 x #s(literal 1/2 binary64)) (if (<=.f64 x #s(literal 6000000000000000578799285889800569438076928 binary64)) z (.f64 x #s(literal 1/2 binary64))))
z

soundness759.0ms (14.5%)

Memory

20.5MiB live, 336.1MiB allocated

Rules

6 434×	`accelerator-lowering-fma.f32`
6 434×	`accelerator-lowering-fma.f64`
5 686×	`accelerator-lowering-fma.f32`
5 686×	`accelerator-lowering-fma.f64`
3 028×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	508
1	200	508
2	512	508
3	1440	508
4	3343	508
5	5374	508
6	7166	508
7	7996	508
0	8046	463
0	57	440
1	174	440
2	488	440
3	1318	440
4	3632	440
5	6705	440
0	8250	412

Stop Event

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

Compiler

Compiled 184 to 99 computations (46.2% saved)

preprocess58.0ms (1.1%)

Memory: 6.1MiB live, 85.6MiB allocated
Compiler: Compiled 240 to 102 computations (57.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

sample1.2s (23%)

preprocess81.0ms (1.6%)

explain94.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.2%)

localize24.0ms (0.5%)

series6.0ms (0.1%)

rewrite363.0ms (6.9%)

simplify216.0ms (4.1%)

eval37.0ms (0.7%)

prune37.0ms (0.7%)

simplify5.0ms (0.1%)

localize32.0ms (0.6%)

series4.0ms (0.1%)

rewrite461.0ms (8.8%)

simplify276.0ms (5.3%)

eval82.0ms (1.6%)

prune147.0ms (2.8%)

simplify4.0ms (0.1%)

localize26.0ms (0.5%)

series1.0ms (0%)

rewrite533.0ms (10.2%)

simplify312.0ms (5.9%)

eval35.0ms (0.7%)

prune117.0ms (2.2%)

regimes20.0ms (0.4%)

regimes10.0ms (0.2%)

regimes75.0ms (1.4%)

regimes7.0ms (0.1%)

regimes32.0ms (0.6%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch34.0ms (0.6%)

bsearch22.0ms (0.4%)

bsearch22.0ms (0.4%)

bsearch28.0ms (0.5%)

bsearch36.0ms (0.7%)

simplify25.0ms (0.5%)

soundness759.0ms (14.5%)

preprocess58.0ms (1.1%)

end0.0ms (0%)

Profiling