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

analyze14.0ms (0.2%)

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: 2.0ms (52.8% of total)

ival-div: 1.0ms (26.4% of total)

const: 0.0ms (0% of total)

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

sample983.0ms (15.5%)

Results

733.0ms	8255×	0	valid
0.0ms	1×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 310.0ms

ival-add: 173.0ms (55.8% of total)

ival-div: 122.0ms (39.4% of total)

const: 12.0ms (3.9% of total)

backward-pass: 3.0ms (1% of total)

Bogosity

preprocess73.0ms (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))

explain61.0ms (1%)

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

35.0ms

512×

valid

Compiler

Compiled 47 to 20 computations (57.4% saved)

Precisions

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

ival-add: 7.0ms (57.6% of total)

ival-div: 4.0ms (32.9% of total)

const: 1.0ms (8.2% 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)

localize23.0ms (0.4%)

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

16.0ms

256×

valid

Compiler

Compiled 19 to 7 computations (63.2% saved)

Precisions

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

ival-add: 4.0ms (66.4% of total)

ival-div: 2.0ms (33.2% of total)

const: 0.0ms (0% of total)

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

series32.0ms (0.5%)

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
29.0ms	x	@	inf	(+ x y)
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	y	@	-inf	(/ (+ x y) (+ y 1))

rewrite340.0ms (5.4%)

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	323	13
3	4035	13
0	8361	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 x (/.f64 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 (+.f64 x y) (-.f64 #s(literal 0 binary64) (-.f64 x y))) (.f64 (+.f64 y #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (-.f64 x y))))
(/.f64 (.f64 (+.f64 x y) (-.f64 #s(literal 0 binary64) (-.f64 x y))) (.f64 (-.f64 #s(literal -1 binary64) y) (-.f64 x y)))
(/.f64 (.f64 (+.f64 x y) (-.f64 #s(literal 0 binary64) (-.f64 x 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)))
(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 y y)) #s(literal -1 binary64)) (.f64 (-.f64 x y) (-.f64 #s(literal -1 binary64) y)))
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(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) y)) (/.f64 (*.f64 y y) (-.f64 #s(literal 1 binary64) y)))
(fma.f64 y #s(literal 1 binary64) #s(literal 1 binary64))
(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 (+.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))))
(.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 #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 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))))

simplify281.0ms (4.4%)

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	338
2	799	325
3	3312	300
0	8536	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 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) 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)) (/ 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 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 #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 x (+.f64 #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 (0.7%)

Compiler: Compiled 8949 to 1036 computations (88.4% saved)

prune130.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	412	9	421
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	412	10	422

Accuracy

100.0%

Counts

422 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64)))
▶	53.3%	(/.f64 (+.f64 x y) y)
▶	46.9%	(/.f64 (+.f64 x y) #s(literal 1 binary64))
	51.2%	(/.f64 y (+.f64 y #s(literal 1 binary64)))
▶	50.0%	(/.f64 x (+.f64 y #s(literal 1 binary64)))
▶	47.1%	(+.f64 x (*.f64 y (-.f64 #s(literal 1 binary64) x)))
	46.9%	(+.f64 x (.f64 y (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 y #s(literal -1 binary64)))))
	53.2%	(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) y))
	35.8%	x
▶	40.9%	#s(literal 1 binary64)

Compiler

Compiled 139 to 96 computations (30.9% saved)

simplify205.0ms (3.2%)

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

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

Rules

2004×	`sum5-define`
1236×	`sum3-define`
1100×	`sum4-define`
1032×	`fnmadd-define`
934×	`fmsub-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	49
1	19	48
2	33	48
3	63	47
4	141	47
5	272	47
6	475	47
7	900	47
8	2942	47
9	4101	47
10	4863	47
11	5349	47
12	5558	47
13	5587	47
14	5619	47
15	5646	47
16	5654	47
0	5654	47

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize197.0ms (3.1%)

Localize:

Found 9 expressions of interest:

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

Results

183.0ms

256×

valid

Compiler

Compiled 54 to 12 computations (77.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 76.0ms

ival-div: 68.0ms (89.4% of total)

ival-add: 4.0ms (5.3% of total)

ival-mult: 2.0ms (2.6% of total)

ival-sub: 1.0ms (1.3% of total)

const: 0.0ms (0% of total)

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

series8.0ms (0.1%)

Counts

8 → 168

Calls

Call 1

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

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

Calls

42 calls:

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

rewrite432.0ms (6.8%)

Algorithm

1×	batch-egg-rewrite

Rules

4226×	`-lowering-.f32`
4226×	`-lowering-.f64`
3596×	`/-lowering-/.f32`
3596×	`/-lowering-/.f64`
1540×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	80	33
2	673	33
3	7961	33
0	8507	33

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 554

Calls

Call 1

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

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

simplify224.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

2910×	`-lowering-.f32`
2910×	`-lowering-.f64`
1872×	`+-lowering-+.f64`
1872×	`+-lowering-+.f32`
1282×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	105	744
1	331	665
2	840	657
3	3182	657
4	7485	657
0	8039	657

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

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

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

eval144.0ms (2.3%)

Compiler: Compiled 16055 to 1462 computations (90.9% saved)

prune143.0ms (2.3%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	825	5	830
Fresh	1	3	4
Picked	2	3	5
Done	0	1	1
Total	828	12	840

Accuracy

100.0%

Counts

840 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64)))
✓	53.3%	(/.f64 (+.f64 x y) y)
	51.2%	(/.f64 y (+.f64 y #s(literal 1 binary64)))
✓	50.0%	(/.f64 x (+.f64 y #s(literal 1 binary64)))
	15.1%	(/.f64 x y)
▶	46.9%	(+.f64 y x)
▶	53.2%	(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) y))
▶	36.0%	(*.f64 x (-.f64 #s(literal 1 binary64) y))
▶	36.0%	(.f64 x (+.f64 (.f64 y (+.f64 y #s(literal -1 binary64))) #s(literal 1 binary64)))
	13.5%	y
▶	35.8%	x
✓	40.9%	#s(literal 1 binary64)

Compiler

Compiled 126 to 88 computations (30.2% saved)

simplify247.0ms (3.9%)

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

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

Rules

3410×	`fnmadd-define`
1980×	`fmsub-define`
1956×	`fnmsub-define`
1832×	`fma-lowering-fma.f32`
1832×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	62
1	38	62
2	85	62
3	219	59
4	391	59
5	689	59
6	1228	59
7	2649	59
8	4289	59
9	4830	59
10	5115	59
11	5670	59
12	6357	59
0	8034	59

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize69.0ms (1.1%)

Localize:

Found 10 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 (*.f64 y (+.f64 y #s(literal -1 binary64))) #s(literal 1 binary64))
✓	accuracy	93.7%	(.f64 x (+.f64 (.f64 y (+.f64 y #s(literal -1 binary64))) #s(literal 1 binary64)))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) y)
✓	accuracy	100.0%	(*.f64 x (-.f64 #s(literal 1 binary64) y))
✓	accuracy	100.0%	(+.f64 y x)
✓	accuracy	100.0%	(+.f64 x #s(literal -1 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) y))
✓	accuracy	100.0%	(/.f64 (+.f64 x #s(literal -1 binary64)) y)

Results

45.0ms

256×

valid

Compiler

Compiled 67 to 15 computations (77.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-add: 7.0ms (44.3% of total)

ival-mult: 5.0ms (31.6% of total)

ival-div: 2.0ms (12.7% of total)

ival-sub: 1.0ms (6.3% of total)

const: 1.0ms (6.3% of total)

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

series31.0ms (0.5%)

Counts

10 → 180

Calls

Call 1

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

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

Calls

45 calls:

Time	Variable		Point	Expression
21.0ms	x	@	0	(/ (+ x -1) y)
2.0ms	x	@	0	(+ 1 (/ (+ x -1) y))
1.0ms	x	@	0	(* x (+ (* y (+ y -1)) 1))
0.0ms	x	@	-inf	(+ 1 (/ (+ x -1) y))
0.0ms	x	@	inf	(+ 1 (/ (+ x -1) y))

rewrite314.0ms (5%)

Algorithm

1×	batch-egg-rewrite

Rules

3582×	`/-lowering-/.f32`
3582×	`/-lowering-/.f64`
3208×	`-lowering-.f32`
3208×	`-lowering-.f64`
2236×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	48
1	103	48
2	957	46
0	8891	46

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 415

Calls

Call 1

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

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

simplify197.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

2050×	`--lowering--.f32`
2050×	`--lowering--.f64`
2018×	`-lowering-.f32`
2018×	`-lowering-.f64`
1766×	`fnmadd-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	869
1	284	821
2	797	764
3	2459	735
4	7019	735
0	8318	735

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

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

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

eval71.0ms (1.1%)

Compiler: Compiled 9732 to 1323 computations (86.4% saved)

prune57.0ms (0.9%)

Pruning

12 alts after pruning (3 fresh and 9 done)

	Pruned	Kept	Total
New	594	1	595
Fresh	1	2	3
Picked	0	5	5
Done	0	4	4
Total	595	12	607

Accuracy

100.0%

Counts

607 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64)))
✓	53.3%	(/.f64 (+.f64 x y) y)
✓	50.0%	(/.f64 x (+.f64 y #s(literal 1 binary64)))
▶	15.1%	(/.f64 x y)
✓	46.9%	(+.f64 y x)
✓	53.2%	(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) y))
▶	40.7%	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))
✓	36.0%	(*.f64 x (-.f64 #s(literal 1 binary64) y))
✓	36.0%	(.f64 x (+.f64 (.f64 y (+.f64 y #s(literal -1 binary64))) #s(literal 1 binary64)))
▶	13.5%	y
✓	35.8%	x
✓	40.9%	#s(literal 1 binary64)

Compiler

Compiled 76 to 54 computations (28.9% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

4×	`+-lowering-+.f64`
4×	`/-lowering-/.f32`
4×	`/-lowering-/.f64`
4×	`+-lowering-+.f32`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	10	17
0	10	17

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize42.0ms (0.7%)

Localize:

Found 3 expressions of interest:

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

Results

35.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-add: 6.0ms (53.9% of total)

ival-div: 4.0ms (36% of total)

const: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Counts

3 → 48

Calls

Call 1

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

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

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	y	@	inf	(/ x y)
0.0ms	x	@	-inf	(/ x y)
0.0ms	y	@	0	(/ -1 y)
0.0ms	y	@	-inf	(/ x y)
0.0ms	x	@	inf	(/ x y)

rewrite177.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1902×	`prod-diff`
1274×	`fma-lowering-fma.f32`
1274×	`fma-lowering-fma.f64`
1130×	`-lowering-.f32`
1130×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	35	11
2	237	10
3	3230	9
0	9428	9

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 152

Calls

Call 1

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

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

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

52×	`sum3-define`
40×	`+-lowering-+.f64`
40×	`+-lowering-+.f32`
28×	`--lowering--.f32`
28×	`sub-neg`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	158
1	19	149
2	26	149
3	36	149
4	47	149
5	62	149
6	85	149
7	103	149
8	121	149
9	132	149
10	139	149
0	139	149

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

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

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

eval46.0ms (0.7%)

Compiler: Compiled 3759 to 345 computations (90.8% saved)

prune28.0ms (0.4%)

Pruning

12 alts after pruning (0 fresh and 12 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	0	0
Picked	0	3	3
Done	0	9	9
Total	200	12	212

Accuracy

100.0%

Counts

212 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64)))
✓	53.3%	(/.f64 (+.f64 x y) y)
✓	50.0%	(/.f64 x (+.f64 y #s(literal 1 binary64)))
✓	15.1%	(/.f64 x y)
✓	46.9%	(+.f64 y x)
✓	53.2%	(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) y))
✓	40.7%	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))
✓	36.0%	(*.f64 x (-.f64 #s(literal 1 binary64) y))
✓	36.0%	(.f64 x (+.f64 (.f64 y (+.f64 y #s(literal -1 binary64))) #s(literal 1 binary64)))
✓	13.5%	y
✓	35.8%	x
✓	40.9%	#s(literal 1 binary64)

Compiler

Compiled 158 to 84 computations (46.8% saved)

regimes23.0ms (0.4%)

Counts

16 → 1

Calls

Call 1

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

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

Calls

3 calls:

12.0ms	x
5.0ms	y
5.0ms	(/.f64 (+.f64 x y) (+.f64 y #s(literal 1 binary64)))

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)

regimes10.0ms (0.2%)

Counts

13 → 3

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	x
4.0ms	y

Results

Accuracy	Segments	Branch
78.9%	3	`x`
97.9%	3	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes7.0ms (0.1%)

Counts

12 → 3

Calls

Call 1

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

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

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
97.2%	3	`y`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes5.0ms (0.1%)

Counts

11 → 3

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
97.0%	3	`y`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes4.0ms (0.1%)

Counts

10 → 5

Calls

Call 1

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
89.2%	5	`y`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes6.0ms (0.1%)

Counts

7 → 3

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
84.7%	3	`y`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes3.0ms (0%)

Counts

6 → 3

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
84.6%	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	x
2.0ms	y

Results

Accuracy	Segments	Branch
54.8%	3	`x`
73.2%	3	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

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:

1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
40.9%	1	`x`
40.9%	1	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch21.0ms (0.3%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.001260245200431137	15.865470157220745
10.0ms	-2.214829938981572	-0.06932005894270565

Results

11.0ms

240×

valid

Compiler

Compiled 314 to 235 computations (25.2% saved)

Precisions

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

ival-div: 2.0ms (42.7% of total)

ival-add: 2.0ms (42.7% of total)

const: 0.0ms (0% of total)

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

bsearch45.0ms (0.7%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.001260245200431137	15.865470157220745
33.0ms	-2.214829938981572	-0.06932005894270565

Results

11.0ms

240×

valid

Compiler

Compiled 254 to 190 computations (25.2% saved)

Precisions

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

ival-div: 2.0ms (43.3% of total)

ival-add: 2.0ms (43.3% of total)

const: 0.0ms (0% of total)

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

bsearch33.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
22.0ms	0.001260245200431137	15.865470157220745
9.0ms	-2.214829938981572	-0.06932005894270565

Results

23.0ms

240×

valid

Compiler

Compiled 224 to 145 computations (35.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-add: 15.0ms (87.8% of total)

ival-div: 2.0ms (11.7% of total)

const: 0.0ms (0% of total)

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

bsearch60.0ms (0.9%)

Algorithm

4×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
26.0ms	4.5307208858365244e+27	1.327177283712887e+32
12.0ms	1.3398185284123273e-19	8.320789546838482e-10
10.0ms	-4.538433528736556e-14	-5.0294719731033974e-17
9.0ms	-4.3633285135098283e+24	-1.403131263714009e+23

Results

34.0ms

528×

valid

Compiler

Compiled 446 to 340 computations (23.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-add: 16.0ms (78.2% of total)

ival-div: 4.0ms (19.5% of total)

const: 1.0ms (4.9% of total)

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

bsearch28.0ms (0.4%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
10.0ms	11244.227955594406	163497667.61466923
9.0ms	-2.214829938981572	-0.06932005894270565

Results

11.0ms

240×

valid

Compiler

Compiled 196 to 154 computations (21.4% saved)

Precisions

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

ival-add: 3.0ms (62.6% of total)

ival-div: 2.0ms (41.7% of total)

const: 0.0ms (0% of total)

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

bsearch21.0ms (0.3%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
10.0ms	11244.227955594406	163497667.61466923
9.0ms	-2.214829938981572	-0.06932005894270565

Results

11.0ms

240×

valid

Compiler

Compiled 164 to 130 computations (20.7% saved)

Precisions

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

ival-add: 3.0ms (61.4% of total)

ival-div: 2.0ms (40.9% of total)

const: 0.0ms (0% of total)

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

bsearch37.0ms (0.6%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
10.0ms	11244.227955594406	163497667.61466923
25.0ms	-2.214829938981572	-0.06932005894270565

Results

28.0ms

240×

valid

Compiler

Compiled 134 to 115 computations (14.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-add: 19.0ms (88.6% of total)

ival-div: 2.0ms (9.3% of total)

const: 0.0ms (0% of total)

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

simplify23.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
10×	`if-if-or-not_binary32`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	139
1	72	139
2	75	139
3	77	139
4	78	139

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 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) y)) (if (<=.f64 y #s(literal 1 binary64)) (+.f64 x (*.f64 y (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) y))))
(if (<=.f64 y #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) y)) (if (<=.f64 y #s(literal 5404319552844595/4503599627370496 binary64)) (+.f64 y x) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) y))))
(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 -569999999999999995805696 binary64)) #s(literal 1 binary64) (if (<=.f64 y #s(literal -3565267313141895/79228162514264337593543950336 binary64)) (/.f64 x (+.f64 y #s(literal 1 binary64))) (if (<=.f64 y #s(literal 7833839311102797/9671406556917033397649408 binary64)) (+.f64 y x) (if (<=.f64 y #s(literal 50000000000000002683081102196736 binary64)) (/.f64 x (+.f64 y #s(literal 1 binary64))) #s(literal 1 binary64)))))
(if (<=.f64 y #s(literal -1 binary64)) #s(literal 1 binary64) (if (<=.f64 y #s(literal 11500 binary64)) (+.f64 y x) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))))
(if (<=.f64 y #s(literal -1 binary64)) #s(literal 1 binary64) (if (<=.f64 y #s(literal 11500 binary64)) (+.f64 y x) #s(literal 1 binary64)))
(if (<=.f64 y #s(literal -1 binary64)) #s(literal 1 binary64) (if (<=.f64 y #s(literal 11500 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 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) y)) (if (<=.f64 y #s(literal 1 binary64)) (+.f64 x (*.f64 y (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) y))))
(if (<=.f64 y #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) y)) (if (<=.f64 y #s(literal 5404319552844595/4503599627370496 binary64)) (+.f64 y x) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) y))))
(if (<=.f64 y #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) y)) (if (<=.f64 y #s(literal 5404319552844595/4503599627370496 binary64)) (+.f64 x y) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) y))))
(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 -569999999999999995805696 binary64)) #s(literal 1 binary64) (if (<=.f64 y #s(literal -3565267313141895/79228162514264337593543950336 binary64)) (/.f64 x (+.f64 y #s(literal 1 binary64))) (if (<=.f64 y #s(literal 7833839311102797/9671406556917033397649408 binary64)) (+.f64 y x) (if (<=.f64 y #s(literal 50000000000000002683081102196736 binary64)) (/.f64 x (+.f64 y #s(literal 1 binary64))) #s(literal 1 binary64)))))
(if (<=.f64 y #s(literal -569999999999999995805696 binary64)) #s(literal 1 binary64) (if (<=.f64 y #s(literal -3565267313141895/79228162514264337593543950336 binary64)) (/.f64 x (+.f64 y #s(literal 1 binary64))) (if (<=.f64 y #s(literal 7833839311102797/9671406556917033397649408 binary64)) (+.f64 x y) (if (<=.f64 y #s(literal 50000000000000002683081102196736 binary64)) (/.f64 x (+.f64 y #s(literal 1 binary64))) #s(literal 1 binary64)))))
(if (<=.f64 y #s(literal -1 binary64)) #s(literal 1 binary64) (if (<=.f64 y #s(literal 11500 binary64)) (+.f64 y x) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))))
(if (<=.f64 y #s(literal -1 binary64)) #s(literal 1 binary64) (if (<=.f64 y #s(literal 11500 binary64)) (+.f64 x y) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))))
(if (<=.f64 y #s(literal -1 binary64)) #s(literal 1 binary64) (if (<=.f64 y #s(literal 11500 binary64)) (+.f64 y x) #s(literal 1 binary64)))
(if (<=.f64 y #s(literal -1 binary64)) #s(literal 1 binary64) (if (<=.f64 y #s(literal 11500 binary64)) (+.f64 x y) #s(literal 1 binary64)))
(if (<=.f64 y #s(literal -1 binary64)) #s(literal 1 binary64) (if (<=.f64 y #s(literal 11500 binary64)) x #s(literal 1 binary64)))
#s(literal 1 binary64)

soundness1.3s (20.5%)

Rules

4226×	`-lowering-.f32`
4226×	`-lowering-.f64`
3596×	`/-lowering-/.f32`
3596×	`/-lowering-/.f64`
2296×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	80	33
2	673	33
3	7961	33
0	8507	33
0	88	353
1	277	338
2	799	325
3	3312	300
0	8536	300
0	94	869
1	284	821
2	797	764
3	2459	735
4	7019	735
0	8318	735

Stop Event

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

Compiler

Compiled 292 to 146 computations (50% saved)

preprocess49.0ms (0.8%)

Compiler: Compiled 332 to 106 computations (68.1% saved)

Iter	Nodes	Cost
0	10	158
1	19	149
2	26	149
3	36	149
4	47	149
5	62	149
6	85	149
7	103	149
8	121	149
9	132	149
10	139	149
0	139	149

Iter	Nodes	Cost
0	10	158
1	19	149
2	26	149
3	36	149
4	47	149
5	62	149
6	85	149
7	103	149
8	121	149
9	132	149
10	139	149
0	139	149

analyze14.0ms (0.2%)

sample983.0ms (15.5%)

preprocess73.0ms (1.2%)

explain61.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize23.0ms (0.4%)

series32.0ms (0.5%)

rewrite340.0ms (5.4%)

simplify281.0ms (4.4%)

eval47.0ms (0.7%)

prune130.0ms (2.1%)

simplify205.0ms (3.2%)

localize197.0ms (3.1%)

series8.0ms (0.1%)

rewrite432.0ms (6.8%)

simplify224.0ms (3.5%)

eval144.0ms (2.3%)

prune143.0ms (2.3%)

simplify247.0ms (3.9%)

localize69.0ms (1.1%)

series31.0ms (0.5%)

rewrite314.0ms (5%)

simplify197.0ms (3.1%)

eval71.0ms (1.1%)

prune57.0ms (0.9%)

simplify5.0ms (0.1%)

localize42.0ms (0.7%)

series5.0ms (0.1%)

rewrite177.0ms (2.8%)

simplify12.0ms (0.2%)

eval46.0ms (0.7%)

prune28.0ms (0.4%)

regimes23.0ms (0.4%)

regimes10.0ms (0.2%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

regimes6.0ms (0.1%)

regimes3.0ms (0%)

regimes4.0ms (0.1%)

regimes3.0ms (0%)

bsearch21.0ms (0.3%)

bsearch45.0ms (0.7%)

bsearch33.0ms (0.5%)

bsearch60.0ms (0.9%)

bsearch28.0ms (0.4%)

bsearch21.0ms (0.3%)

bsearch37.0ms (0.6%)

simplify23.0ms (0.4%)

soundness1.3s (20.5%)

preprocess49.0ms (0.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	10	158
1	19	149
2	26	149
3	36	149
4	47	149
5	62	149
6	85	149
7	103	149
8	121	149
9	132	149
10	139	149
0	139	149