Metrics for Data.Colour.SRGB:invTransferFunction from colour-2.3.3

analyze19.0ms (0.3%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
75%	74.9%	25%	0.1%	0%	0%	0%	5
75%	74.9%	25%	0.1%	0%	0%	0%	6
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	7
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	8
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	9
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	10
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	11
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	12

Compiler

Compiled 10 to 7 computations (30% saved)

Precisions

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

ival-add: 3.0ms (73.5% of total)

ival-div: 1.0ms (24.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample1.0s (17.1%)

Results

862.0ms	8252×	0	valid
0.0ms	2×	2	valid
0.0ms	2×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 316.0ms

ival-add: 213.0ms (67.3% of total)

ival-div: 87.0ms (27.5% of total)

const: 13.0ms (4.1% of total)

backward-pass: 3.0ms (0.9% of total)

Bogosity

preprocess72.0ms (1.2%)

Algorithm

2×	egg-herbie

Rules

2850×	`fnmadd-define`
1856×	`sum4-define`
1640×	`sum3-define`
1478×	`fnmsub-define`
1444×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	48
1	44	42
2	91	42
3	230	42
4	786	42
5	2444	42
6	5598	42
7	6340	42
8	7672	42
0	6	7
1	10	7
0	10	7

Stop Event

1×	iter limit
1×	saturated
1×	node limit

Calls

Call 1

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

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

Call 2

Inputs
(/ (+ x y) (+ y 1))
(/ (+ (neg x) y) (+ y 1))
(/ (+ x (neg y)) (+ (neg y) 1))
(neg (/ (+ (neg x) y) (+ y 1)))
(neg (/ (+ x (neg y)) (+ (neg y) 1)))
(/ (+ y x) (+ x 1))

Outputs
(/ (+ x y) (+ y 1))
(/ (+ (neg x) y) (+ y 1))
(/ (- y x) (+ y 1))
(/ (+ x (neg y)) (+ (neg y) 1))
(/ (- y x) (+ y -1))
(neg (/ (+ (neg x) y) (+ y 1)))
(/ (- y x) (- -1 y))
(neg (/ (+ x (neg y)) (+ (neg y) 1)))
(/ (- y x) (- 1 y))
(/ (+ y x) (+ x 1))
(/ (+ x y) (+ x 1))

explain80.0ms (1.3%)

FPErrors

Click to see full error table

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

Results

62.0ms

512×

valid

Compiler

Compiled 47 to 20 computations (57.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-div: 15.0ms (51.5% of total)

ival-add: 13.0ms (44.6% of total)

const: 1.0ms (3.4% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

8×	`+-lowering-+.f64`
8×	`+-lowering-+.f32`
4×	`+-commutative`
2×	`/-lowering-/.f32`
2×	`/-lowering-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	10	16
0	10	16

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize46.0ms (0.8%)

Localize:

Found 3 expressions of interest:

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

Results

39.0ms

256×

valid

Compiler

Compiled 19 to 7 computations (63.2% saved)

Precisions

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

ival-div: 3.0ms (50.1% of total)

ival-add: 3.0ms (50.1% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series3.0ms (0.1%)

Counts

3 → 60

Calls

Call 1

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

Outputs
#<alt (/ y (+ 1 y))>
#<alt (+ (/ x (+ 1 y)) (/ y (+ 1 y)))>
#<alt (+ (/ x (+ 1 y)) (/ y (+ 1 y)))>
#<alt (+ (/ x (+ 1 y)) (/ y (+ 1 y)))>
#<alt (/ x (+ 1 y))>
#<alt (* x (+ (/ 1 (+ 1 y)) (/ y (* x (+ 1 y)))))>
#<alt (* x (+ (/ 1 (+ 1 y)) (/ y (* x (+ 1 y)))))>
#<alt (* x (+ (/ 1 (+ 1 y)) (/ y (* x (+ 1 y)))))>
#<alt (/ x (+ 1 y))>
#<alt (* -1 (* x (- (* -1 (/ y (* x (+ 1 y)))) (/ 1 (+ 1 y)))))>
#<alt (* -1 (* x (- (* -1 (/ y (* x (+ 1 y)))) (/ 1 (+ 1 y)))))>
#<alt (* -1 (* x (- (* -1 (/ y (* x (+ 1 y)))) (/ 1 (+ 1 y)))))>
#<alt x>
#<alt (+ x (* y (- 1 x)))>
#<alt (+ x (* y (- (+ 1 (* y (- x 1))) x)))>
#<alt (+ x (* y (- (+ 1 (* y (- (+ x (* y (- 1 x))) 1))) x)))>
#<alt 1>
#<alt (- (+ 1 (/ x y)) (/ 1 y))>
#<alt (- (+ 1 (+ (/ 1 (pow y 2)) (/ x y))) (+ (/ 1 y) (/ x (pow y 2))))>
#<alt (- (+ 1 (+ (/ 1 (pow y 2)) (+ (/ x y) (/ x (pow y 3))))) (+ (/ 1 y) (+ (/ 1 (pow y 3)) (/ x (pow y 2)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (+ 1 (* -1 x)) y)))>
#<alt (+ 1 (* -1 (/ (+ 1 (+ (* -1 x) (* -1 (/ (+ 1 (* -1 x)) y)))) y)))>
#<alt (+ 1 (* -1 (/ (+ 1 (+ (* -1 x) (* -1 (/ (- (* -1 (/ (+ 1 (* -1 x)) y)) (* -1 (+ 1 (* -1 x)))) y)))) y)))>
#<alt y>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt x>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt x>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt y>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt 1>
#<alt (+ 1 y)>
#<alt (+ 1 y)>
#<alt (+ 1 y)>
#<alt y>
#<alt (* y (+ 1 (/ 1 y)))>
#<alt (* y (+ 1 (/ 1 y)))>
#<alt (* y (+ 1 (/ 1 y)))>
#<alt y>
#<alt (* y (+ 1 (/ 1 y)))>
#<alt (* y (+ 1 (/ 1 y)))>
#<alt (* y (+ 1 (/ 1 y)))>

Calls

15 calls:

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

rewrite425.0ms (7%)

Algorithm

1×	batch-egg-rewrite

Rules

3592×	`-lowering-.f32`
3592×	`-lowering-.f64`
2366×	`fma-lowering-fma.f32`
2366×	`fma-lowering-fma.f64`
2232×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	40	13
2	325	13
3	4045	13
0	8441	13

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 361

Calls

Call 1

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

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

simplify247.0ms (4%)

Algorithm

1×	egg-herbie

Rules

2296×	`+-lowering-+.f64`
2296×	`+-lowering-+.f32`
1894×	`-lowering-.f32`
1894×	`-lowering-.f64`
1804×	`fmsub-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	353
1	277	332
2	800	322
3	3317	300
0	8543	300

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
(/ y (+ 1 y))
(+ (/ x (+ 1 y)) (/ y (+ 1 y)))
(+ (/ x (+ 1 y)) (/ y (+ 1 y)))
(+ (/ x (+ 1 y)) (/ y (+ 1 y)))
(/ x (+ 1 y))
(* x (+ (/ 1 (+ 1 y)) (/ y (* x (+ 1 y)))))
(* x (+ (/ 1 (+ 1 y)) (/ y (* x (+ 1 y)))))
(* x (+ (/ 1 (+ 1 y)) (/ y (* x (+ 1 y)))))
(/ x (+ 1 y))
(* -1 (* x (- (* -1 (/ y (* x (+ 1 y)))) (/ 1 (+ 1 y)))))
(* -1 (* x (- (* -1 (/ y (* x (+ 1 y)))) (/ 1 (+ 1 y)))))
(* -1 (* x (- (* -1 (/ y (* x (+ 1 y)))) (/ 1 (+ 1 y)))))
x
(+ x (* y (- 1 x)))
(+ x (* y (- (+ 1 (* y (- x 1))) x)))
(+ x (* y (- (+ 1 (* y (- (+ x (* y (- 1 x))) 1))) x)))
1
(- (+ 1 (/ x y)) (/ 1 y))
(- (+ 1 (+ (/ 1 (pow y 2)) (/ x y))) (+ (/ 1 y) (/ x (pow y 2))))
(- (+ 1 (+ (/ 1 (pow y 2)) (+ (/ x y) (/ x (pow y 3))))) (+ (/ 1 y) (+ (/ 1 (pow y 3)) (/ x (pow y 2)))))
1
(+ 1 (* -1 (/ (+ 1 (* -1 x)) y)))
(+ 1 (* -1 (/ (+ 1 (+ (* -1 x) (* -1 (/ (+ 1 (* -1 x)) y)))) y)))
(+ 1 (* -1 (/ (+ 1 (+ (* -1 x) (* -1 (/ (- (* -1 (/ (+ 1 (* -1 x)) y)) (* -1 (+ 1 (* -1 x)))) y)))) y)))
y
(+ x y)
(+ x y)
(+ x y)
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
x
(+ x y)
(+ x y)
(+ x y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
1
(+ 1 y)
(+ 1 y)
(+ 1 y)
y
(* y (+ 1 (/ 1 y)))
(* y (+ 1 (/ 1 y)))
(* y (+ 1 (/ 1 y)))
y
(* y (+ 1 (/ 1 y)))
(* y (+ 1 (/ 1 y)))
(* y (+ 1 (/ 1 y)))

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

eval47.0ms (0.8%)

Compiler: Compiled 8947 to 1033 computations (88.5% saved)

prune78.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	414	7	421
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	414	8	422

Accuracy

100.0%

Counts

422 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64)))
	46.9%	(/.f64 (+.f64 x y) y)
	55.2%	(/.f64 (+.f64 x y) #s(literal 1 binary64))
▶	50.2%	(/.f64 y (+.f64 y #s(literal 1 binary64)))
▶	51.2%	(/.f64 x (+.f64 y #s(literal 1 binary64)))
▶	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y #s(literal 1 binary64)) (+.f64 x y)))
▶	39.7%	x
▶	35.2%	#s(literal 1 binary64)

Compiler

Compiled 99 to 68 computations (31.3% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

64×	`-lowering-.f32`
64×	`-lowering-.f64`
48×	`fma-define`
42×	`/-lowering-/.f32`
42×	`/-lowering-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	47
1	16	47
2	28	46
3	52	46
4	82	46
5	91	46
6	106	46
7	120	46
8	129	46
9	152	46
10	154	46
0	154	46

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize81.0ms (1.3%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 y #s(literal 1 binary64))
✓	accuracy	100.0%	(/.f64 y (+.f64 y #s(literal 1 binary64)))
✓	accuracy	100.0%	(+.f64 y #s(literal 1 binary64))
✓	accuracy	100.0%	(/.f64 x (+.f64 y #s(literal 1 binary64)))
✓	accuracy	100.0%	(+.f64 y #s(literal 1 binary64))
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(/.f64 (+.f64 y #s(literal 1 binary64)) (+.f64 x y))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y #s(literal 1 binary64)) (+.f64 x y)))

Results

67.0ms

256×

valid

Compiler

Compiled 51 to 10 computations (80.4% saved)

Precisions

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

ival-div: 8.0ms (70.5% of total)

ival-add: 3.0ms (26.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series6.0ms (0.1%)

Counts

6 → 120

Calls

Call 1

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

Outputs
#<alt x>
#<alt (+ x (* y (- 1 x)))>
#<alt (+ x (* y (- (+ 1 (* y (- x 1))) x)))>
#<alt (+ x (* y (- (+ 1 (* y (- (+ x (* y (- 1 x))) 1))) x)))>
#<alt 1>
#<alt (- (+ 1 (/ x y)) (/ 1 y))>
#<alt (- (+ 1 (+ (/ 1 (pow y 2)) (/ x y))) (+ (/ 1 y) (/ x (pow y 2))))>
#<alt (- (+ 1 (+ (/ 1 (pow y 2)) (+ (/ x y) (/ x (pow y 3))))) (+ (/ 1 y) (+ (/ 1 (pow y 3)) (/ x (pow y 2)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (+ 1 (* -1 x)) y)))>
#<alt (+ 1 (* -1 (/ (+ 1 (+ (* -1 x) (* -1 (/ (+ 1 (* -1 x)) y)))) y)))>
#<alt (+ 1 (* -1 (/ (+ 1 (+ (* -1 x) (* -1 (/ (- (* -1 (/ (+ 1 (* -1 x)) y)) (* -1 (+ 1 (* -1 x)))) y)))) y)))>
#<alt (/ y (+ 1 y))>
#<alt (+ (/ x (+ 1 y)) (/ y (+ 1 y)))>
#<alt (+ (/ x (+ 1 y)) (/ y (+ 1 y)))>
#<alt (+ (/ x (+ 1 y)) (/ y (+ 1 y)))>
#<alt (/ x (+ 1 y))>
#<alt (* x (+ (/ 1 (+ 1 y)) (/ y (* x (+ 1 y)))))>
#<alt (* x (+ (/ 1 (+ 1 y)) (/ y (* x (+ 1 y)))))>
#<alt (* x (+ (/ 1 (+ 1 y)) (/ y (* x (+ 1 y)))))>
#<alt (/ x (+ 1 y))>
#<alt (* -1 (* x (- (* -1 (/ y (* x (+ 1 y)))) (/ 1 (+ 1 y)))))>
#<alt (* -1 (* x (- (* -1 (/ y (* x (+ 1 y)))) (/ 1 (+ 1 y)))))>
#<alt (* -1 (* x (- (* -1 (/ y (* x (+ 1 y)))) (/ 1 (+ 1 y)))))>
#<alt (/ 1 x)>
#<alt (+ (* y (- (/ 1 x) (/ 1 (pow x 2)))) (/ 1 x))>
#<alt (+ (* y (- (+ (* y (- (/ 1 (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x)) (/ 1 (pow x 2)))) (/ 1 x))>
#<alt (+ (* y (- (+ (* y (- (+ (* y (- (/ 1 (pow x 3)) (/ 1 (pow x 4)))) (/ 1 (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x)) (/ 1 (pow x 2)))) (/ 1 x))>
#<alt 1>
#<alt (- (+ 1 (/ 1 y)) (/ x y))>
#<alt (- (+ 1 (+ (* -1 (/ (* x (- 1 x)) (pow y 2))) (/ 1 y))) (/ x y))>
#<alt (- (+ 1 (+ (/ 1 y) (/ (* (pow x 2) (- 1 x)) (pow y 3)))) (+ (/ x y) (/ (* x (- 1 x)) (pow y 2))))>
#<alt 1>
#<alt (+ 1 (+ (* -1 (/ x y)) (/ 1 y)))>
#<alt (+ 1 (* -1 (/ (- (/ (* x (+ 1 (* -1 x))) y) (+ 1 (* -1 x))) y)))>
#<alt (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (* (pow x 2) (+ 1 (* -1 x))) y) (* x (+ 1 (* -1 x)))) y)) (+ 1 (* -1 x))) y)))>
#<alt (/ (+ 1 y) y)>
#<alt (+ 1 (+ (* -1 (* x (+ (/ 1 y) (/ 1 (pow y 2))))) (/ 1 y)))>
#<alt (+ 1 (+ (* x (- (/ (* x (+ (/ 1 y) (/ 1 (pow y 2)))) y) (+ (/ 1 y) (/ 1 (pow y 2))))) (/ 1 y)))>
#<alt (+ 1 (+ (* x (- (* x (- (* -1 (* x (+ (/ 1 (pow y 3)) (/ 1 (pow y 4))))) (* -1 (/ (+ (/ 1 y) (/ 1 (pow y 2))) y)))) (+ (/ 1 y) (/ 1 (pow y 2))))) (/ 1 y)))>
#<alt (/ (+ 1 y) x)>
#<alt (/ (+ 1 (+ y (* -1 (/ (* y (+ 1 y)) x)))) x)>
#<alt (/ (- (+ 1 (+ y (/ (* (pow y 2) (+ 1 y)) (pow x 2)))) (/ (* y (+ 1 y)) x)) x)>
#<alt (/ (- (+ 1 (+ y (* -1 (/ (* (pow y 3) (+ 1 y)) (pow x 3))))) (+ (* -1 (/ (* (pow y 2) (+ 1 y)) (pow x 2))) (/ (* y (+ 1 y)) x))) x)>
#<alt (/ (+ 1 y) x)>
#<alt (* -1 (/ (+ (* -1 (+ 1 y)) (/ (* y (+ 1 y)) x)) x))>
#<alt (* -1 (/ (+ (* -1 (+ 1 y)) (* -1 (/ (- (/ (* (pow y 2) (+ 1 y)) x) (* y (+ 1 y))) x))) x))>
#<alt (* -1 (/ (+ (* -1 (+ 1 y)) (* -1 (/ (- (* -1 (/ (- (/ (* (pow y 3) (+ 1 y)) x) (* (pow y 2) (+ 1 y))) x)) (* y (+ 1 y))) x))) x))>
#<alt 1>
#<alt (+ 1 y)>
#<alt (+ 1 y)>
#<alt (+ 1 y)>
#<alt y>
#<alt (* y (+ 1 (/ 1 y)))>
#<alt (* y (+ 1 (/ 1 y)))>
#<alt (* y (+ 1 (/ 1 y)))>
#<alt y>
#<alt (* y (+ 1 (/ 1 y)))>
#<alt (* y (+ 1 (/ 1 y)))>
#<alt (* y (+ 1 (/ 1 y)))>
#<alt y>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt x>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt x>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt y>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt x>
#<alt (+ x (* -1 (* x y)))>
#<alt (+ x (* y (- (* x y) x)))>
#<alt (+ x (* y (- (* y (- (* -1 (* x y)) (* -1 x))) x)))>
#<alt (/ x y)>
#<alt (/ (+ x (* -1 (/ x y))) y)>
#<alt (/ (- (+ x (/ x (pow y 2))) (/ x y)) y)>
#<alt (/ (- (+ x (* -1 (/ x (pow y 3)))) (+ (* -1 (/ x (pow y 2))) (/ x y))) y)>
#<alt (/ x y)>
#<alt (* -1 (/ (+ (* -1 x) (/ x y)) y))>
#<alt (* -1 (/ (+ (* -1 x) (* -1 (/ (- (/ x y) x) y))) y))>
#<alt (* -1 (/ (+ (* -1 x) (* -1 (/ (- (* -1 (/ (- (/ x y) x) y)) x) y))) y))>
#<alt y>
#<alt (* y (+ 1 (* -1 y)))>
#<alt (* y (+ 1 (* y (- y 1))))>
#<alt (* y (+ 1 (* y (- (* y (+ 1 (* -1 y))) 1))))>
#<alt 1>
#<alt (- 1 (/ 1 y))>
#<alt (- (+ 1 (/ 1 (pow y 2))) (/ 1 y))>
#<alt (- (+ 1 (/ 1 (pow y 2))) (+ (/ 1 y) (/ 1 (pow y 3))))>
#<alt 1>
#<alt (- 1 (/ 1 y))>
#<alt (+ 1 (* -1 (/ (- 1 (/ 1 y)) y)))>
#<alt (+ 1 (* -1 (/ (+ 1 (* -1 (/ (- 1 (/ 1 y)) y))) y)))>

Calls

30 calls:

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

rewrite320.0ms (5.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3410×	`-lowering-.f32`
3410×	`-lowering-.f64`
3108×	`/-lowering-/.f32`
3108×	`/-lowering-/.f64`
1176×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	31
1	64	30
2	470	30
3	6050	30
0	8259	30

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 700

Calls

Call 1

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

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

simplify256.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

3882×	`-lowering-.f32`
3882×	`-lowering-.f64`
3130×	`+-lowering-+.f64`
3130×	`+-lowering-+.f32`
1740×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	270	1109
1	910	1001
2	2710	949
0	8530	949

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
x
(+ x (* y (- 1 x)))
(+ x (* y (- (+ 1 (* y (- x 1))) x)))
(+ x (* y (- (+ 1 (* y (- (+ x (* y (- 1 x))) 1))) x)))
1
(- (+ 1 (/ x y)) (/ 1 y))
(- (+ 1 (+ (/ 1 (pow y 2)) (/ x y))) (+ (/ 1 y) (/ x (pow y 2))))
(- (+ 1 (+ (/ 1 (pow y 2)) (+ (/ x y) (/ x (pow y 3))))) (+ (/ 1 y) (+ (/ 1 (pow y 3)) (/ x (pow y 2)))))
1
(+ 1 (* -1 (/ (+ 1 (* -1 x)) y)))
(+ 1 (* -1 (/ (+ 1 (+ (* -1 x) (* -1 (/ (+ 1 (* -1 x)) y)))) y)))
(+ 1 (* -1 (/ (+ 1 (+ (* -1 x) (* -1 (/ (- (* -1 (/ (+ 1 (* -1 x)) y)) (* -1 (+ 1 (* -1 x)))) y)))) y)))
(/ y (+ 1 y))
(+ (/ x (+ 1 y)) (/ y (+ 1 y)))
(+ (/ x (+ 1 y)) (/ y (+ 1 y)))
(+ (/ x (+ 1 y)) (/ y (+ 1 y)))
(/ x (+ 1 y))
(* x (+ (/ 1 (+ 1 y)) (/ y (* x (+ 1 y)))))
(* x (+ (/ 1 (+ 1 y)) (/ y (* x (+ 1 y)))))
(* x (+ (/ 1 (+ 1 y)) (/ y (* x (+ 1 y)))))
(/ x (+ 1 y))
(* -1 (* x (- (* -1 (/ y (* x (+ 1 y)))) (/ 1 (+ 1 y)))))
(* -1 (* x (- (* -1 (/ y (* x (+ 1 y)))) (/ 1 (+ 1 y)))))
(* -1 (* x (- (* -1 (/ y (* x (+ 1 y)))) (/ 1 (+ 1 y)))))
(/ 1 x)
(+ (* y (- (/ 1 x) (/ 1 (pow x 2)))) (/ 1 x))
(+ (* y (- (+ (* y (- (/ 1 (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x)) (/ 1 (pow x 2)))) (/ 1 x))
(+ (* y (- (+ (* y (- (+ (* y (- (/ 1 (pow x 3)) (/ 1 (pow x 4)))) (/ 1 (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x)) (/ 1 (pow x 2)))) (/ 1 x))
1
(- (+ 1 (/ 1 y)) (/ x y))
(- (+ 1 (+ (* -1 (/ (* x (- 1 x)) (pow y 2))) (/ 1 y))) (/ x y))
(- (+ 1 (+ (/ 1 y) (/ (* (pow x 2) (- 1 x)) (pow y 3)))) (+ (/ x y) (/ (* x (- 1 x)) (pow y 2))))
1
(+ 1 (+ (* -1 (/ x y)) (/ 1 y)))
(+ 1 (* -1 (/ (- (/ (* x (+ 1 (* -1 x))) y) (+ 1 (* -1 x))) y)))
(+ 1 (* -1 (/ (- (* -1 (/ (- (/ (* (pow x 2) (+ 1 (* -1 x))) y) (* x (+ 1 (* -1 x)))) y)) (+ 1 (* -1 x))) y)))
(/ (+ 1 y) y)
(+ 1 (+ (* -1 (* x (+ (/ 1 y) (/ 1 (pow y 2))))) (/ 1 y)))
(+ 1 (+ (* x (- (/ (* x (+ (/ 1 y) (/ 1 (pow y 2)))) y) (+ (/ 1 y) (/ 1 (pow y 2))))) (/ 1 y)))
(+ 1 (+ (* x (- (* x (- (* -1 (* x (+ (/ 1 (pow y 3)) (/ 1 (pow y 4))))) (* -1 (/ (+ (/ 1 y) (/ 1 (pow y 2))) y)))) (+ (/ 1 y) (/ 1 (pow y 2))))) (/ 1 y)))
(/ (+ 1 y) x)
(/ (+ 1 (+ y (* -1 (/ (* y (+ 1 y)) x)))) x)
(/ (- (+ 1 (+ y (/ (* (pow y 2) (+ 1 y)) (pow x 2)))) (/ (* y (+ 1 y)) x)) x)
(/ (- (+ 1 (+ y (* -1 (/ (* (pow y 3) (+ 1 y)) (pow x 3))))) (+ (* -1 (/ (* (pow y 2) (+ 1 y)) (pow x 2))) (/ (* y (+ 1 y)) x))) x)
(/ (+ 1 y) x)
(* -1 (/ (+ (* -1 (+ 1 y)) (/ (* y (+ 1 y)) x)) x))
(* -1 (/ (+ (* -1 (+ 1 y)) (* -1 (/ (- (/ (* (pow y 2) (+ 1 y)) x) (* y (+ 1 y))) x))) x))
(* -1 (/ (+ (* -1 (+ 1 y)) (* -1 (/ (- (* -1 (/ (- (/ (* (pow y 3) (+ 1 y)) x) (* (pow y 2) (+ 1 y))) x)) (* y (+ 1 y))) x))) x))
1
(+ 1 y)
(+ 1 y)
(+ 1 y)
y
(* y (+ 1 (/ 1 y)))
(* y (+ 1 (/ 1 y)))
(* y (+ 1 (/ 1 y)))
y
(* y (+ 1 (/ 1 y)))
(* y (+ 1 (/ 1 y)))
(* y (+ 1 (/ 1 y)))
y
(+ x y)
(+ x y)
(+ x y)
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
x
(+ x y)
(+ x y)
(+ x y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
x
(+ x (* -1 (* x y)))
(+ x (* y (- (* x y) x)))
(+ x (* y (- (* y (- (* -1 (* x y)) (* -1 x))) x)))
(/ x y)
(/ (+ x (* -1 (/ x y))) y)
(/ (- (+ x (/ x (pow y 2))) (/ x y)) y)
(/ (- (+ x (* -1 (/ x (pow y 3)))) (+ (* -1 (/ x (pow y 2))) (/ x y))) y)
(/ x y)
(* -1 (/ (+ (* -1 x) (/ x y)) y))
(* -1 (/ (+ (* -1 x) (* -1 (/ (- (/ x y) x) y))) y))
(* -1 (/ (+ (* -1 x) (* -1 (/ (- (* -1 (/ (- (/ x y) x) y)) x) y))) y))
y
(* y (+ 1 (* -1 y)))
(* y (+ 1 (* y (- y 1))))
(* y (+ 1 (* y (- (* y (+ 1 (* -1 y))) 1))))
1
(- 1 (/ 1 y))
(- (+ 1 (/ 1 (pow y 2))) (/ 1 y))
(- (+ 1 (/ 1 (pow y 2))) (+ (/ 1 y) (/ 1 (pow y 3))))
1
(- 1 (/ 1 y))
(+ 1 (* -1 (/ (- 1 (/ 1 y)) y)))
(+ 1 (* -1 (/ (+ 1 (* -1 (/ (- 1 (/ 1 y)) y))) y)))

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

eval243.0ms (4%)

Compiler: Compiled 19665 to 2229 computations (88.7% saved)

prune257.0ms (4.2%)

Pruning

10 alts after pruning (5 fresh and 5 done)

	Pruned	Kept	Total
New	1001	3	1004
Fresh	0	2	2
Picked	1	4	5
Done	0	1	1
Total	1002	10	1012

Accuracy

100.0%

Counts

1012 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64)))
▶	46.9%	(/.f64 (+.f64 x y) y)
▶	55.2%	(/.f64 (+.f64 x y) #s(literal 1 binary64))
✓	50.2%	(/.f64 y (+.f64 y #s(literal 1 binary64)))
✓	51.2%	(/.f64 x (+.f64 y #s(literal 1 binary64)))
▶	14.9%	(/.f64 x y)
▶	51.1%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y #s(literal 1 binary64)) x))
▶	18.2%	y
✓	39.7%	x
✓	35.2%	#s(literal 1 binary64)

Compiler

Compiled 91 to 61 computations (33% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

68×	`-lowering-.f32`
68×	`-lowering-.f64`
52×	`fma-define`
50×	`/-lowering-/.f32`
50×	`/-lowering-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	42
1	17	42
2	24	41
3	30	41
4	57	41
5	80	41
6	97	41
7	126	41
8	147	41
9	155	41
10	158	41
0	158	41

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize258.0ms (4.2%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 y #s(literal 1 binary64))
✓	accuracy	100.0%	(/.f64 (+.f64 y #s(literal 1 binary64)) x)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y #s(literal 1 binary64)) x))
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(/.f64 (+.f64 x y) y)
✓	accuracy	100.0%	(/.f64 x y)
✓	accuracy	100.0%	(/.f64 (+.f64 x y) #s(literal 1 binary64))
✓	accuracy	100.0%	(+.f64 x y)

Results

244.0ms

256×

valid

Compiler

Compiled 48 to 11 computations (77.1% saved)

Precisions

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

ival-div: 9.0ms (72.4% of total)

ival-add: 3.0ms (24.1% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series19.0ms (0.3%)

Counts

7 → 156

Calls

Call 1

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

Outputs
#<alt y>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt x>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt x>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt y>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt y>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt x>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt x>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt y>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 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 1>
#<alt (+ 1 (/ x y))>
#<alt (+ 1 (/ x y))>
#<alt (+ 1 (/ x y))>
#<alt (/ x y)>
#<alt (* x (+ (/ 1 x) (/ 1 y)))>
#<alt (* x (+ (/ 1 x) (/ 1 y)))>
#<alt (* x (+ (/ 1 x) (/ 1 y)))>
#<alt (/ x y)>
#<alt (* x (+ (/ 1 x) (/ 1 y)))>
#<alt (* x (+ (/ 1 x) (/ 1 y)))>
#<alt (* x (+ (/ 1 x) (/ 1 y)))>
#<alt (/ x y)>
#<alt (/ (+ x y) y)>
#<alt (/ (+ x y) y)>
#<alt (/ (+ x y) y)>
#<alt 1>
#<alt (+ 1 (/ x y))>
#<alt (+ 1 (/ x y))>
#<alt (+ 1 (/ x y))>
#<alt 1>
#<alt (+ 1 (/ x y))>
#<alt (+ 1 (/ x y))>
#<alt (+ 1 (/ x y))>
#<alt x>
#<alt (+ x (* -1 (* x y)))>
#<alt (+ x (* y (- (* x y) x)))>
#<alt (+ x (* y (- (* y (- (* -1 (* x y)) (* -1 x))) x)))>
#<alt (/ x y)>
#<alt (/ (+ x (* -1 (/ x y))) y)>
#<alt (/ (- (+ x (/ x (pow y 2))) (/ x y)) y)>
#<alt (/ (- (+ x (* -1 (/ x (pow y 3)))) (+ (* -1 (/ x (pow y 2))) (/ x y))) y)>
#<alt (/ x y)>
#<alt (* -1 (/ (+ (* -1 x) (/ x y)) y))>
#<alt (* -1 (/ (+ (* -1 x) (* -1 (/ (- (/ x y) x) y))) y))>
#<alt (* -1 (/ (+ (* -1 x) (* -1 (/ (- (* -1 (/ (- (/ x y) x) y)) x) y))) y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ x (+ 1 y))>
#<alt (/ 1 x)>
#<alt (+ (/ 1 x) (/ y x))>
#<alt (+ (/ 1 x) (/ y x))>
#<alt (+ (/ 1 x) (/ y x))>
#<alt (/ y x)>
#<alt (* y (+ (/ 1 x) (/ 1 (* x y))))>
#<alt (* y (+ (/ 1 x) (/ 1 (* x y))))>
#<alt (* y (+ (/ 1 x) (/ 1 (* x y))))>
#<alt (/ y x)>
#<alt (* y (+ (/ 1 x) (/ 1 (* x y))))>
#<alt (* y (+ (/ 1 x) (/ 1 (* x y))))>
#<alt (* y (+ (/ 1 x) (/ 1 (* x y))))>
#<alt (/ (+ 1 y) x)>
#<alt (/ (+ 1 y) x)>
#<alt (/ (+ 1 y) x)>
#<alt (/ (+ 1 y) x)>
#<alt (/ (+ 1 y) x)>
#<alt (/ (+ 1 y) x)>
#<alt (/ (+ 1 y) x)>
#<alt (/ (+ 1 y) x)>
#<alt (/ (+ 1 y) x)>
#<alt (/ (+ 1 y) x)>
#<alt (/ (+ 1 y) x)>
#<alt (/ (+ 1 y) x)>
#<alt 1>
#<alt (+ 1 y)>
#<alt (+ 1 y)>
#<alt (+ 1 y)>
#<alt y>
#<alt (* y (+ 1 (/ 1 y)))>
#<alt (* y (+ 1 (/ 1 y)))>
#<alt (* y (+ 1 (/ 1 y)))>
#<alt y>
#<alt (* y (+ 1 (/ 1 y)))>
#<alt (* y (+ 1 (/ 1 y)))>
#<alt (* y (+ 1 (/ 1 y)))>

Calls

39 calls:

Time	Variable		Point	Expression
12.0ms	y	@	inf	(/ (+ x y) y)
1.0ms	y	@	-inf	(/ x y)
1.0ms	x	@	inf	(/ x y)
0.0ms	x	@	-inf	(/ x y)
0.0ms	y	@	-inf	(/ (+ x y) y)

rewrite523.0ms (8.6%)

Algorithm

1×	batch-egg-rewrite

Rules

2586×	`-lowering-.f32`
2586×	`-lowering-.f64`
2504×	`/-lowering-/.f32`
2504×	`/-lowering-/.f64`
2482×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	71	27
2	512	27
3	5041	27
0	8281	27

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 637

Calls

Call 1

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

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

simplify268.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

2580×	`-lowering-.f32`
2580×	`-lowering-.f64`
1992×	`fmsub-define`
1820×	`fmm-def`
1816×	`fnmsub-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	636
1	242	618
2	541	612
3	2160	588
0	8272	588

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

Inputs
y
(+ x y)
(+ x y)
(+ x y)
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
x
(+ x y)
(+ x y)
(+ x y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
y
(+ x y)
(+ x y)
(+ x y)
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
x
(+ x y)
(+ x y)
(+ x y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 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)
1
(+ 1 (/ x y))
(+ 1 (/ x y))
(+ 1 (/ x y))
(/ x y)
(* x (+ (/ 1 x) (/ 1 y)))
(* x (+ (/ 1 x) (/ 1 y)))
(* x (+ (/ 1 x) (/ 1 y)))
(/ x y)
(* x (+ (/ 1 x) (/ 1 y)))
(* x (+ (/ 1 x) (/ 1 y)))
(* x (+ (/ 1 x) (/ 1 y)))
(/ x y)
(/ (+ x y) y)
(/ (+ x y) y)
(/ (+ x y) y)
1
(+ 1 (/ x y))
(+ 1 (/ x y))
(+ 1 (/ x y))
1
(+ 1 (/ x y))
(+ 1 (/ x y))
(+ 1 (/ x y))
x
(+ x (* -1 (* x y)))
(+ x (* y (- (* x y) x)))
(+ x (* y (- (* y (- (* -1 (* x y)) (* -1 x))) x)))
(/ x y)
(/ (+ x (* -1 (/ x y))) y)
(/ (- (+ x (/ x (pow y 2))) (/ x y)) y)
(/ (- (+ x (* -1 (/ x (pow y 3)))) (+ (* -1 (/ x (pow y 2))) (/ x y))) y)
(/ x y)
(* -1 (/ (+ (* -1 x) (/ x y)) y))
(* -1 (/ (+ (* -1 x) (* -1 (/ (- (/ x y) x) y))) y))
(* -1 (/ (+ (* -1 x) (* -1 (/ (- (* -1 (/ (- (/ x y) x) y)) x) y))) y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ x (+ 1 y))
(/ 1 x)
(+ (/ 1 x) (/ y x))
(+ (/ 1 x) (/ y x))
(+ (/ 1 x) (/ y x))
(/ y x)
(* y (+ (/ 1 x) (/ 1 (* x y))))
(* y (+ (/ 1 x) (/ 1 (* x y))))
(* y (+ (/ 1 x) (/ 1 (* x y))))
(/ y x)
(* y (+ (/ 1 x) (/ 1 (* x y))))
(* y (+ (/ 1 x) (/ 1 (* x y))))
(* y (+ (/ 1 x) (/ 1 (* x y))))
(/ (+ 1 y) x)
(/ (+ 1 y) x)
(/ (+ 1 y) x)
(/ (+ 1 y) x)
(/ (+ 1 y) x)
(/ (+ 1 y) x)
(/ (+ 1 y) x)
(/ (+ 1 y) x)
(/ (+ 1 y) x)
(/ (+ 1 y) x)
(/ (+ 1 y) x)
(/ (+ 1 y) x)
1
(+ 1 y)
(+ 1 y)
(+ 1 y)
y
(* y (+ 1 (/ 1 y)))
(* y (+ 1 (/ 1 y)))
(* y (+ 1 (/ 1 y)))
y
(* y (+ 1 (/ 1 y)))
(* y (+ 1 (/ 1 y)))
(* y (+ 1 (/ 1 y)))

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

eval144.0ms (2.4%)

Compiler: Compiled 14930 to 1520 computations (89.8% saved)

prune145.0ms (2.4%)

Pruning

10 alts after pruning (1 fresh and 9 done)

	Pruned	Kept	Total
New	910	1	911
Fresh	0	0	0
Picked	1	4	5
Done	0	5	5
Total	911	10	921

Accuracy

100.0%

Counts

921 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64)))
✓	46.9%	(/.f64 (+.f64 x y) y)
✓	50.2%	(/.f64 y (+.f64 y #s(literal 1 binary64)))
✓	51.2%	(/.f64 x (+.f64 y #s(literal 1 binary64)))
✓	14.9%	(/.f64 x y)
✓	51.1%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y #s(literal 1 binary64)) x))
▶	55.2%	(+.f64 y x)
✓	18.2%	y
✓	39.7%	x
✓	35.2%	#s(literal 1 binary64)

Compiler

Compiled 58 to 39 computations (32.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
1	4	5
0	4	5

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ y x)
y
x

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

localize17.0ms (0.3%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 y x)

Results

12.0ms

256×

valid

Compiler

Compiled 8 to 4 computations (50% saved)

Precisions

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

ival-add: 2.0ms (98.9% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series0.0ms (0%)

Counts

1 → 24

Calls

Call 1

Inputs
#<alt (+ y x)>

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

Calls

6 calls:

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

rewrite312.0ms (5.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2570×	`/-lowering-/.f32`
2570×	`/-lowering-/.f64`
2334×	`-lowering-.f32`
2334×	`-lowering-.f64`
2168×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	17	3
2	143	3
3	1437	3
0	8273	3

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 129

Calls

Call 1

Inputs
(+ y x)

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

simplify144.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

2204×	`fnmadd-define`
1784×	`sum3-define`
1612×	`fma-define`
1168×	`fma-lowering-fma.f32`
1168×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	60
1	61	60
2	141	60
3	414	60
4	1439	60
5	3143	60
6	5012	60
7	7893	60
0	8027	60

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

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

Outputs
x
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
y
(* y (+ 1 (/ x y)))
(+.f64 x y)
(* y (+ 1 (/ x y)))
(+.f64 x y)
(* y (+ 1 (/ x y)))
(+.f64 x y)
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 x y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 x y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 x y)
y
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
x
(* x (+ 1 (/ y x)))
(+.f64 x y)
(* x (+ 1 (/ y x)))
(+.f64 x y)
(* x (+ 1 (/ y x)))
(+.f64 x y)
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 x y)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 x y)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 x y)

eval17.0ms (0.3%)

Compiler: Compiled 4858 to 418 computations (91.4% saved)

prune20.0ms (0.3%)

Pruning

10 alts after pruning (0 fresh and 10 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	0	0
Picked	0	1	1
Done	0	9	9
Total	153	10	163

Accuracy

100.0%

Counts

163 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64)))
✓	46.9%	(/.f64 (+.f64 x y) y)
✓	50.2%	(/.f64 y (+.f64 y #s(literal 1 binary64)))
✓	51.2%	(/.f64 x (+.f64 y #s(literal 1 binary64)))
✓	14.9%	(/.f64 x y)
✓	51.1%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y #s(literal 1 binary64)) x))
✓	55.2%	(+.f64 y x)
✓	18.2%	y
✓	39.7%	x
✓	35.2%	#s(literal 1 binary64)

Compiler

Compiled 112 to 55 computations (50.9% saved)

regimes15.0ms (0.2%)

Counts

12 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	(/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64)))
4.0ms	x
4.0ms	y

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0.1%)

Counts

10 → 3

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	y
4.0ms	x

Results

Accuracy	Segments	Branch
78.9%	3	`x`
98.9%	3	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0.1%)

Counts

8 → 3

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
87.3%	3	`y`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes3.0ms (0.1%)

Counts

6 → 3

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
87.0%	3	`y`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes4.0ms (0.1%)

Counts

3 → 3

Calls

Call 1

Inputs
#s(literal 1 binary64)
x
y

Outputs
#s(literal 1 binary64)
x
#s(literal 1 binary64)

Calls

2 calls:

2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
58.5%	5	`x`
71.0%	3	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

Calls

2 calls:

3.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
35.2%	1	`x`
35.2%	1	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch31.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
15.0ms	2.163253323164153e-6	36684.67990495839
13.0ms	-531704248592.04614	-1.1840617826632218e-5

Results

19.0ms

320×

valid

Compiler

Compiled 294 to 190 computations (35.4% saved)

Precisions

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

ival-div: 3.0ms (45.9% of total)

ival-add: 3.0ms (45.9% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch40.0ms (0.7%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	2.163253323164153e-6	36684.67990495839
22.0ms	-531704248592.04614	-1.1840617826632218e-5

Results

25.0ms

320×

valid

Compiler

Compiled 294 to 210 computations (28.6% saved)

Precisions

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

ival-add: 3.0ms (46.4% of total)

ival-div: 2.0ms (31% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch32.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
16.0ms	2.163253323164153e-6	36684.67990495839
13.0ms	-531704248592.04614	-1.1840617826632218e-5

Results

20.0ms

320×

valid

Compiler

Compiled 214 to 170 computations (20.6% saved)

Precisions

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

ival-add: 3.0ms (46.6% of total)

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch32.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	2.163253323164153e-6	36684.67990495839
16.0ms	-531704248592.04614	-1.1840617826632218e-5

Results

20.0ms

320×

valid

Compiler

Compiled 174 to 150 computations (13.8% saved)

Precisions

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

ival-div: 3.0ms (45.7% of total)

ival-add: 3.0ms (45.7% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`if-if-or-not_binary32`
4×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	66
1	46	66

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64)))
(if (<=.f64 y #s(literal -1 binary64)) (/.f64 (+.f64 x y) y) (if (<=.f64 y #s(literal 1 binary64)) (+.f64 y x) (/.f64 (+.f64 x y) y)))
(if (<=.f64 y #s(literal -7378697629483821/295147905179352825856 binary64)) (/.f64 y (+.f64 y #s(literal 1 binary64))) (if (<=.f64 y #s(literal 2184094498327211/590295810358705651712 binary64)) (+.f64 y x) (/.f64 y (+.f64 y #s(literal 1 binary64)))))
(if (<=.f64 y #s(literal -1 binary64)) #s(literal 1 binary64) (if (<=.f64 y #s(literal 24 binary64)) (+.f64 y x) #s(literal 1 binary64)))
(if (<=.f64 y #s(literal -1 binary64)) #s(literal 1 binary64) (if (<=.f64 y #s(literal 8669429282688205/1125899906842624 binary64)) x #s(literal 1 binary64)))
#s(literal 1 binary64)

Outputs
(/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64)))
(if (<=.f64 y #s(literal -1 binary64)) (/.f64 (+.f64 x y) y) (if (<=.f64 y #s(literal 1 binary64)) (+.f64 y x) (/.f64 (+.f64 x y) y)))
(if (<=.f64 y #s(literal -1 binary64)) (/.f64 (+.f64 x y) y) (if (<=.f64 y #s(literal 1 binary64)) (+.f64 x y) (/.f64 (+.f64 x y) y)))
(if (<=.f64 y #s(literal -7378697629483821/295147905179352825856 binary64)) (/.f64 y (+.f64 y #s(literal 1 binary64))) (if (<=.f64 y #s(literal 2184094498327211/590295810358705651712 binary64)) (+.f64 y x) (/.f64 y (+.f64 y #s(literal 1 binary64)))))
(if (<=.f64 y #s(literal -7378697629483821/295147905179352825856 binary64)) (/.f64 y (+.f64 y #s(literal 1 binary64))) (if (<=.f64 y #s(literal 2184094498327211/590295810358705651712 binary64)) (+.f64 x y) (/.f64 y (+.f64 y #s(literal 1 binary64)))))
(if (<=.f64 y #s(literal -1 binary64)) #s(literal 1 binary64) (if (<=.f64 y #s(literal 24 binary64)) (+.f64 y x) #s(literal 1 binary64)))
(if (<=.f64 y #s(literal -1 binary64)) #s(literal 1 binary64) (if (<=.f64 y #s(literal 24 binary64)) (+.f64 x y) #s(literal 1 binary64)))
(if (<=.f64 y #s(literal -1 binary64)) #s(literal 1 binary64) (if (<=.f64 y #s(literal 8669429282688205/1125899906842624 binary64)) x #s(literal 1 binary64)))
#s(literal 1 binary64)

soundness736.0ms (12.1%)

Rules

2586×	`-lowering-.f32`
2586×	`-lowering-.f64`
2504×	`/-lowering-/.f32`
2504×	`/-lowering-/.f64`
2482×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	71	27
2	512	27
3	5041	27
0	8281	27
0	88	353
1	277	332
2	800	322
3	3317	300
0	8543	300

Stop Event

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

Compiler

Compiled 138 to 71 computations (48.6% saved)

preprocess53.0ms (0.9%)

Compiler: Compiled 170 to 66 computations (61.2% saved)

Iter	Nodes	Cost
0	9	47
1	16	47
2	28	46
3	52	46
4	82	46
5	91	46
6	106	46
7	120	46
8	129	46
9	152	46
10	154	46
0	154	46

Iter	Nodes	Cost
0	10	42
1	17	42
2	24	41
3	30	41
4	57	41
5	80	41
6	97	41
7	126	41
8	147	41
9	155	41
10	158	41
0	158	41

Iter	Nodes	Cost
0	9	47
1	16	47
2	28	46
3	52	46
4	82	46
5	91	46
6	106	46
7	120	46
8	129	46
9	152	46
10	154	46
0	154	46

Iter	Nodes	Cost
0	10	42
1	17	42
2	24	41
3	30	41
4	57	41
5	80	41
6	97	41
7	126	41
8	147	41
9	155	41
10	158	41
0	158	41

analyze19.0ms (0.3%)

sample1.0s (17.1%)

preprocess72.0ms (1.2%)

explain80.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize46.0ms (0.8%)

series3.0ms (0.1%)

rewrite425.0ms (7%)

simplify247.0ms (4%)

eval47.0ms (0.8%)

prune78.0ms (1.3%)

simplify10.0ms (0.2%)

localize81.0ms (1.3%)

series6.0ms (0.1%)

rewrite320.0ms (5.2%)

simplify256.0ms (4.2%)

eval243.0ms (4%)

prune257.0ms (4.2%)

simplify11.0ms (0.2%)

localize258.0ms (4.2%)

series19.0ms (0.3%)

rewrite523.0ms (8.6%)

simplify268.0ms (4.4%)

eval144.0ms (2.4%)

prune145.0ms (2.4%)

simplify4.0ms (0.1%)

localize17.0ms (0.3%)

series0.0ms (0%)

rewrite312.0ms (5.1%)

simplify144.0ms (2.4%)

eval17.0ms (0.3%)

prune20.0ms (0.3%)

regimes15.0ms (0.2%)

regimes9.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

regimes4.0ms (0.1%)

regimes5.0ms (0.1%)

bsearch31.0ms (0.5%)

bsearch40.0ms (0.7%)

bsearch32.0ms (0.5%)

bsearch32.0ms (0.5%)

simplify12.0ms (0.2%)

soundness736.0ms (12.1%)

preprocess53.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	9	47
1	16	47
2	28	46
3	52	46
4	82	46
5	91	46
6	106	46
7	120	46
8	129	46
9	152	46
10	154	46
0	154	46

Iter	Nodes	Cost
0	10	42
1	17	42
2	24	41
3	30	41
4	57	41
5	80	41
6	97	41
7	126	41
8	147	41
9	155	41
10	158	41
0	158	41