Metrics for Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, A

analyze0.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 10 to 8 computations (20% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

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

const: 0.0ms (0% of total)

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

sample776.0ms (9.5%)

Results

486.0ms	7601×	0	valid
36.0ms	212×	2	valid
34.0ms	302×	1	valid
26.0ms	141×	3	valid

Precisions

Click to see histograms. Total time spent on operations: 271.0ms

ival-div: 96.0ms (35.4% of total)

ival-mult: 96.0ms (35.4% of total)

ival-sub: 51.0ms (18.8% of total)

const: 15.0ms (5.5% of total)

backward-pass: 13.0ms (4.8% of total)

Bogosity

preprocess49.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

296×	`fnmsub-define`
296×	`fmsub-define`
296×	`fnmadd-define`
204×	`fnmadd-define`
198×	`fmm-def`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	34
1	48	32
2	96	26
3	230	24
4	545	24
5	930	24
6	1068	24
7	1080	24
0	8	5
1	15	5
2	25	4
3	41	4
4	59	4
5	100	4
6	181	4
7	285	4
8	364	4
9	561	4
10	681	4
11	695	4
0	695	4

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- x (* (/ 3 8) y))

Outputs
(- x (* (/ 3 8) y))
(+.f64 x (*.f64 y #s(literal -3/8 binary64)))

Call 2

Inputs
(- x (* (/ 3 8) y))
(- (neg x) (* (/ 3 8) y))
(- x (* (/ 3 8) (neg y)))
(neg (- (neg x) (* (/ 3 8) y)))
(neg (- x (* (/ 3 8) (neg y))))
(- y (* (/ 3 8) x))

Outputs
(- x (* (/ 3 8) y))
(fma y -3/8 x)
(- (neg x) (* (/ 3 8) y))
(fnmsub 3/8 y x)
(- x (* (/ 3 8) (neg y)))
(fma 3/8 y x)
(neg (- (neg x) (* (/ 3 8) y)))
(fma 3/8 y x)
(neg (- x (* (/ 3 8) (neg y))))
(fnmsub 3/8 y x)
(- y (* (/ 3 8) x))
(fma x -3/8 y)

explain163.0ms (2%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(-.f64 x (*.f64 (/.f64 #s(literal 3 binary64) #s(literal 8 binary64)) y))`
-	-	`(*.f64 (/.f64 #s(literal 3 binary64) #s(literal 8 binary64)) y)`
-	-	`(/.f64 #s(literal 3 binary64) #s(literal 8 binary64))`
-	-	`#s(literal 3 binary64)`
-	-	`#s(literal 8 binary64)`
-	-	`y`

Results

55.0ms	478×	0	valid
2.0ms	18×	1	valid
2.0ms	10×	2	valid
2.0ms	6×	3	valid

Compiler

Compiled 53 to 23 computations (56.6% saved)

Precisions

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

ival-div: 4.0ms (30.7% of total)

ival-mult: 4.0ms (30.7% of total)

ival-sub: 3.0ms (23% of total)

const: 1.0ms (7.7% of total)

backward-pass: 1.0ms (7.7% of total)

eval0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(+.f64 x (*.f64 y #s(literal -3/8 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 y #s(literal -3/8 binary64))
✓	cost-diff	0	(+.f64 x (*.f64 y #s(literal -3/8 binary64)))

Rules

4×	`fma-lowering-fma.f32`
4×	`fma-define`
4×	`+-lowering-+.f64`
4×	`-lowering-.f32`
4×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	7	10
2	9	10
0	9	10

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ x (* y -3/8))
x
(* y -3/8)
y
-3/8

Outputs
(+ x (* y -3/8))
(+.f64 x (*.f64 y #s(literal -3/8 binary64)))
x
(* y -3/8)
(*.f64 y #s(literal -3/8 binary64))
y
-3/8
#s(literal -3/8 binary64)

localize20.0ms (0.2%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 y #s(literal -3/8 binary64))
✓	accuracy	99.9%	(+.f64 x (*.f64 y #s(literal -3/8 binary64)))

Results

11.0ms	239×	0	valid
1.0ms	9×	1	valid
1.0ms	5×	2	valid
1.0ms	3×	3	valid

Compiler

Compiled 14 to 6 computations (57.1% saved)

Precisions

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

ival-mult: 2.0ms (44.9% of total)

ival-add: 2.0ms (44.9% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

Counts

2 → 36

Calls

Call 1

Inputs
#<alt (+ x (* y -3/8))>
#<alt (* y -3/8)>

Outputs
#<alt (* -3/8 y)>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt x>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt x>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (* -3/8 y)>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* -3/8 y)>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	(* y -3/8)
0.0ms	y	@	inf	(+ x (* y -3/8))
0.0ms	y	@	inf	(* y -3/8)
0.0ms	x	@	inf	(+ x (* y -3/8))
0.0ms	x	@	0	(+ x (* y -3/8))

rewrite349.0ms (4.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3044×	`-lowering-.f32`
3044×	`-lowering-.f64`
2620×	`/-lowering-/.f32`
2620×	`/-lowering-/.f64`
1656×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	20	7
2	177	7
3	1925	7
0	8564	7

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 124

Calls

Call 1

Inputs
(+ x (* y -3/8))
(* y -3/8)

Outputs
(+.f64 x (*.f64 y #s(literal -3/8 binary64)))
(+.f64 (*.f64 y #s(literal -3/8 binary64)) x)
(+.f64 (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (*.f64 y #s(literal -3/8 binary64))))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (.f64 y #s(literal -3/8 binary64))))) #s(literal -1 binary64)))
(-.f64 (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (*.f64 y #s(literal -3/8 binary64)))))
(-.f64 (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (+.f64 (.f64 (.f64 y y) #s(literal -9/64 binary64)) (.f64 y (.f64 y #s(literal 9/64 binary64))))) (-.f64 x (*.f64 y #s(literal -3/8 binary64)))))
(-.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (/.f64 (.f64 x x) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x)))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 27/512 binary64)))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))))) (/.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64))) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 27/512 binary64)))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 9/64 binary64))))))) (-.f64 x (.f64 y #s(literal -3/8 binary64)))) (/.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 9/64 binary64))))))) (-.f64 x (*.f64 y #s(literal -3/8 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 9/64 binary64))))) (-.f64 x (.f64 y #s(literal -3/8 binary64)))) (/.f64 (/.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 81/4096 binary64)) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 9/64 binary64))))) (-.f64 x (*.f64 y #s(literal -3/8 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)))))) (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x)))))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (/.f64 (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64))) (-.f64 #s(literal 0 binary64) (-.f64 x (*.f64 y #s(literal -3/8 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)))) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 27/512 binary64))))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64))) (.f64 (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)))) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (*.f64 y y)) #s(literal 27/512 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 9/64 binary64)))))))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64))) (.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (+.f64 (.f64 x x) (.f64 y (*.f64 y #s(literal 9/64 binary64)))))))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 9/64 binary64)))))) (/.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 81/4096 binary64)) (.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (+.f64 (.f64 x x) (.f64 y (*.f64 y #s(literal 9/64 binary64)))))))
(-.f64 (/.f64 (.f64 (.f64 x x) (-.f64 x (.f64 y #s(literal -3/8 binary64)))) (.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (/.f64 (.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (.f64 y (.f64 y #s(literal 9/64 binary64)))) (.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (-.f64 x (*.f64 y #s(literal -3/8 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (.f64 (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))))) (+.f64 (.f64 (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64)))))) (+.f64 (.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (.f64 (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64)))))))) (/.f64 (.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64)))) (.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64)))))) (+.f64 (.f64 (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64)))))) (+.f64 (.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (.f64 (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (*.f64 y #s(literal -3/8 binary64)))))))))
(-.f64 (/.f64 (.f64 (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64)))))) (+.f64 (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64)))))) (/.f64 (.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (+.f64 (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64)))))))
(fma.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64)))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64))))))
(fma.f64 y #s(literal -3/8 binary64) x)
(fma.f64 #s(literal -3/8 binary64) y x)
(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 y #s(literal -3/8 binary64)))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (*.f64 y #s(literal -3/8 binary64))))))
(fma.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64)))) (+.f64 x (.f64 y #s(literal -3/8 binary64))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64))))))
(fma.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 27/512 binary64)))) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal -3/8 binary64)) (+.f64 x (.f64 y #s(literal -3/8 binary64))))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (*.f64 y #s(literal -3/8 binary64))))))
(neg.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x)))))))
(neg.f64 (/.f64 (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64))) (-.f64 #s(literal 0 binary64) (-.f64 x (.f64 y #s(literal -3/8 binary64))))))
(neg.f64 (-.f64 (/.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))))) (+.f64 x (*.f64 y #s(literal -3/8 binary64)))))
(neg.f64 (-.f64 (/.f64 #s(literal 0 binary64) (-.f64 x (.f64 y #s(literal -3/8 binary64)))) (+.f64 x (.f64 y #s(literal -3/8 binary64)))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x)))))
(/.f64 (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64))))
(/.f64 (+.f64 (.f64 (.f64 y (.f64 y y)) #s(literal 27/512 binary64)) (neg.f64 (.f64 x (.f64 x x)))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64)))) (-.f64 #s(literal 0 binary64) (-.f64 x (.f64 y #s(literal -3/8 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) #s(literal -19683/134217728 binary64))) (.f64 (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64)) (-.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64)) (.f64 x (.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y #s(literal -3/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y #s(literal -3/8 binary64)))) #s(literal 1 binary64)))
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(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))))))) (neg.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (*.f64 y y)) #s(literal 27/512 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 y #s(literal -3/8 binary64)))))) (neg.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 9/64 binary64))))))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 81/4096 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 y #s(literal -3/8 binary64)))))) (neg.f64 (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 9/64 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (.f64 (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))))) (pow.f64 (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64))))) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64)))))) (-.f64 (.f64 (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64)))))) (.f64 (.f64 x (/.f64 x (-.f64 x (.f64 y #s(literal -3/8 binary64))))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 x (*.f64 y #s(literal -3/8 binary64)))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))) (+.f64 (.f64 (/.f64 (.f64 x x) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (/.f64 (.f64 x x) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))) (.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (/.f64 (.f64 x x) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y #s(literal -3/8 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y #s(literal -3/8 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (.f64 y #s(literal -3/8 binary64)) x) (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x))) #s(literal -1 binary64))
(.f64 (+.f64 x (.f64 y #s(literal -3/8 binary64))) (.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y #s(literal -3/8 binary64))))))
(.f64 (+.f64 x (.f64 y #s(literal -3/8 binary64))) (/.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (-.f64 x (.f64 y #s(literal -3/8 binary64)))))
(.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))))))
(.f64 (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)))) (.f64 (+.f64 x (.f64 y #s(literal -3/8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x)))))))
(.f64 (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)))) (/.f64 (+.f64 x (.f64 y #s(literal -3/8 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))))))
(.f64 (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y #s(literal -3/8 binary64)))))
(.f64 (+.f64 (.f64 (.f64 y (.f64 y y)) #s(literal 27/512 binary64)) (neg.f64 (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)))))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x (*.f64 y #s(literal -3/8 binary64))))))
(.f64 #s(literal 1 binary64) (+.f64 x (.f64 y #s(literal -3/8 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))))) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 y #s(literal -3/8 binary64)))) (+.f64 (.f64 x x) (.f64 (*.f64 y y) #s(literal -9/64 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 y #s(literal -3/8 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (*.f64 y y) #s(literal -9/64 binary64)))) #s(literal -1 binary64)))
(.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x)))
(.f64 (/.f64 (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64))) (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64)))) (+.f64 x (.f64 y #s(literal -3/8 binary64))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64)) (.f64 (-.f64 (.f64 y #s(literal -3/8 binary64)) x) (.f64 (-.f64 (.f64 y #s(literal -3/8 binary64)) x) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))) (-.f64 (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))) (*.f64 x x)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 (-.f64 (.f64 y #s(literal -3/8 binary64)) x) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))))) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 3/8 binary64)) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x))))
(.f64 (/.f64 (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64))) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 27/512 binary64)))) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal -3/8 binary64)) (+.f64 x (*.f64 y #s(literal -3/8 binary64))))))
(.f64 (pow.f64 (/.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 9/64 binary64))))))))
(.f64 (pow.f64 (/.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 81/4096 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 9/64 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) #s(literal -19683/134217728 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64)) (-.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64)) (.f64 x (.f64 x x)))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal -3/8 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (*.f64 y y)) #s(literal 27/512 binary64)))))
(exp.f64 (log.f64 (*.f64 y #s(literal -3/8 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 y #s(literal -3/8 binary64))) #s(literal 1 binary64)))
(pow.f64 (*.f64 y #s(literal -3/8 binary64)) #s(literal 1 binary64))
(*.f64 y #s(literal -3/8 binary64))
(*.f64 #s(literal -3/8 binary64) y)
(*.f64 #s(literal -3/8 binary64) (pow.f64 y #s(literal 1 binary64)))
(*.f64 (pow.f64 y #s(literal 1 binary64)) #s(literal -3/8 binary64))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 #s(literal -3/8 binary64))))
(*.f64 (exp.f64 (log.f64 #s(literal -3/8 binary64))) (exp.f64 (log.f64 y)))

simplify238.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1744×	`fnmadd-define`
1606×	`fmsub-define`
1582×	`fnmsub-define`
1436×	`fmm-def`
1428×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	138
1	66	120
2	186	120
3	499	120
4	1449	120
5	4063	120
6	6264	120
0	8007	120

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
(* -3/8 y)
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(+ x (* -3/8 y))
x
(* x (+ 1 (* -3/8 (/ y x))))
(* x (+ 1 (* -3/8 (/ y x))))
(* x (+ 1 (* -3/8 (/ y x))))
x
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
x
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(* -3/8 y)
(* y (- (/ x y) 3/8))
(* y (- (/ x y) 3/8))
(* y (- (/ x y) 3/8))
(* -3/8 y)
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)

Outputs
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
x
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
x
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
x
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* y (- (/ x y) 3/8))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(* y (- (/ x y) 3/8))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(* y (- (/ x y) 3/8))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)

eval25.0ms (0.3%)

Compiler: Compiled 5059 to 416 computations (91.8% saved)

prune23.0ms (0.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	153	7	160
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	153	8	161

Accuracy

100.0%

Counts

161 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 y #s(literal -3/8 binary64) x)
▶	57.9%	(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x)) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))
	27.8%	(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 81/4096 binary64))) (.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 9/64 binary64))))))
▶	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y #s(literal -3/8 binary64)))))
✓	99.9%	(+.f64 x (*.f64 y #s(literal -3/8 binary64)))
	99.6%	(.f64 (+.f64 x (.f64 y #s(literal -3/8 binary64))) (.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y #s(literal -3/8 binary64))))))
▶	52.1%	(*.f64 #s(literal -3/8 binary64) y)
▶	48.8%	x

Compiler

Compiled 203 to 121 computations (40.4% saved)

simplify190.0ms (2.3%)

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 y #s(literal 9/64 binary64))
✓	cost-diff	0	(.f64 y (.f64 y #s(literal 9/64 binary64)))
✓	cost-diff	0	(-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x))
✓	cost-diff	0	(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x)) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))
✓	cost-diff	0	(*.f64 y #s(literal -3/8 binary64))
✓	cost-diff	0	(+.f64 x (*.f64 y #s(literal -3/8 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y #s(literal -3/8 binary64))))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y #s(literal -3/8 binary64)))))
✓	cost-diff	0	(*.f64 #s(literal -3/8 binary64) y)
✓	cost-diff	6272	(fma.f64 y #s(literal -3/8 binary64) x)

Rules

2370×	`fnmadd-define`
1884×	`fma-define`
1536×	`sum5-define`
1488×	`sum4-define`
1260×	`sum3-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	73
1	42	70
2	83	70
3	147	70
4	299	70
5	676	70
6	1920	70
7	3629	70
8	5323	70
9	7359	70
10	7596	70
11	7598	70
12	7613	70
13	7632	70
14	7640	70
0	7640	70

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* y -3/8) x)
y
-3/8
x
x
(* -3/8 y)
-3/8
y
(/ 1 (/ 1 (+ x (* y -3/8))))
1
(/ 1 (+ x (* y -3/8)))
(+ x (* y -3/8))
x
(* y -3/8)
y
-3/8
(/ (- (* y (* y 9/64)) (* x x)) (- (* y -3/8) x))
(- (* y (* y 9/64)) (* x x))
(* y (* y 9/64))
y
(* y 9/64)
9/64
(* x x)
x
(- (* y -3/8) x)
(* y -3/8)
-3/8

Outputs
(+ (* y -3/8) x)
(+.f64 (*.f64 y #s(literal -3/8 binary64)) x)
y
-3/8
#s(literal -3/8 binary64)
x
x
(* -3/8 y)
(*.f64 y #s(literal -3/8 binary64))
-3/8
#s(literal -3/8 binary64)
y
(/ 1 (/ 1 (+ x (* y -3/8))))
(+.f64 (*.f64 y #s(literal -3/8 binary64)) x)
1
#s(literal 1 binary64)
(/ 1 (+ x (* y -3/8)))
(/.f64 #s(literal -1 binary64) (-.f64 (*.f64 y #s(literal 3/8 binary64)) x))
(+ x (* y -3/8))
(+.f64 (*.f64 y #s(literal -3/8 binary64)) x)
x
(* y -3/8)
(*.f64 y #s(literal -3/8 binary64))
y
-3/8
#s(literal -3/8 binary64)
(/ (- (* y (* y 9/64)) (* x x)) (- (* y -3/8) x))
(/.f64 (-.f64 (.f64 #s(literal 9/64 binary64) (.f64 y y)) (.f64 x x)) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))
(- (* y (* y 9/64)) (* x x))
(-.f64 (.f64 #s(literal 9/64 binary64) (.f64 y y)) (*.f64 x x))
(* y (* y 9/64))
(.f64 #s(literal 9/64 binary64) (.f64 y y))
y
(* y 9/64)
(*.f64 y #s(literal 9/64 binary64))
9/64
#s(literal 9/64 binary64)
(* x x)
(*.f64 x x)
x
(- (* y -3/8) x)
(-.f64 (*.f64 y #s(literal -3/8 binary64)) x)
(* y -3/8)
(*.f64 y #s(literal -3/8 binary64))
-3/8
#s(literal -3/8 binary64)

localize122.0ms (1.5%)

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(-.f64 (*.f64 y #s(literal -3/8 binary64)) x)
✓	accuracy	99.7%	(.f64 y (.f64 y #s(literal 9/64 binary64)))
✓	accuracy	96.9%	(-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x))
✓	accuracy	58.5%	(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x)) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))
✓	accuracy	100.0%	(*.f64 y #s(literal -3/8 binary64))
✓	accuracy	99.9%	(+.f64 x (*.f64 y #s(literal -3/8 binary64)))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y #s(literal -3/8 binary64))))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y #s(literal -3/8 binary64)))))
✓	accuracy	100.0%	(*.f64 #s(literal -3/8 binary64) y)
✓	accuracy	100.0%	(fma.f64 y #s(literal -3/8 binary64) x)

Results

54.0ms	220×	0	valid
12.0ms	10×	2	valid
9.0ms	10×	3	valid
5.0ms	14×	1	valid
2.0ms	2×	5	exit

Compiler

Compiled 91 to 18 computations (80.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-mult: 22.0ms (49.7% of total)

ival-div: 7.0ms (15.8% of total)

compiled-spec: 5.0ms (11.3% of total)

ival-sub: 3.0ms (6.8% of total)

backward-pass: 3.0ms (6.8% of total)

ival-add: 3.0ms (6.8% of total)

const: 1.0ms (2.3% of total)

series11.0ms (0.1%)

Counts

11 → 216

Calls

Call 1

Inputs
#<alt (+ (* y -3/8) x)>
#<alt (* -3/8 y)>
#<alt (/ 1 (/ 1 (+ x (* y -3/8))))>
#<alt (/ 1 (+ x (* y -3/8)))>
#<alt (+ x (* y -3/8))>
#<alt (* y -3/8)>
#<alt (/ (- (* y (* y 9/64)) (* x x)) (- (* y -3/8) x))>
#<alt (- (* y (* y 9/64)) (* x x))>
#<alt (* y (* y 9/64))>
#<alt (* y 9/64)>
#<alt (- (* y -3/8) x)>

Outputs
#<alt x>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (* -3/8 y)>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* -3/8 y)>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -3/8 y)>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt x>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt x>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt x>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (* -3/8 y)>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* -3/8 y)>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (/ -8/3 y)>
#<alt (- (* -64/9 (/ x (pow y 2))) (* 8/3 (/ 1 y)))>
#<alt (- (* x (- (* -512/27 (/ x (pow y 3))) (* 64/9 (/ 1 (pow y 2))))) (* 8/3 (/ 1 y)))>
#<alt (- (* x (- (* x (- (* -4096/81 (/ x (pow y 4))) (* 512/27 (/ 1 (pow y 3))))) (* 64/9 (/ 1 (pow y 2))))) (* 8/3 (/ 1 y)))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* 3/8 (/ y x))) x)>
#<alt (/ (- (+ 1 (* 9/64 (/ (pow y 2) (pow x 2)))) (* -3/8 (/ y x))) x)>
#<alt (/ (- (+ 1 (* 27/512 (/ (pow y 3) (pow x 3)))) (+ (* -3/8 (/ y x)) (* -9/64 (/ (pow y 2) (pow x 2))))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (* -3/8 (/ y x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 9/64 (/ (pow y 2) x)) (* -3/8 y)) x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -27/512 (/ (pow y 3) x)) (* 9/64 (pow y 2))) x)) (* -3/8 y)) x)) 1) x))>
#<alt (/ 1 x)>
#<alt (+ (* 3/8 (/ y (pow x 2))) (/ 1 x))>
#<alt (+ (* y (+ (* 9/64 (/ y (pow x 3))) (* 3/8 (/ 1 (pow x 2))))) (/ 1 x))>
#<alt (+ (* y (+ (* y (+ (* 27/512 (/ y (pow x 4))) (* 9/64 (/ 1 (pow x 3))))) (* 3/8 (/ 1 (pow x 2))))) (/ 1 x))>
#<alt (/ -8/3 y)>
#<alt (/ (- (* -64/9 (/ x y)) 8/3) y)>
#<alt (/ (- (* -512/27 (/ (pow x 2) (pow y 2))) (+ 8/3 (* 64/9 (/ x y)))) y)>
#<alt (/ (- (* -4096/81 (/ (pow x 3) (pow y 3))) (+ 8/3 (+ (* 64/9 (/ x y)) (* 512/27 (/ (pow x 2) (pow y 2)))))) y)>
#<alt (/ -8/3 y)>
#<alt (* -1 (/ (+ 8/3 (* 64/9 (/ x y))) y))>
#<alt (* -1 (/ (+ 8/3 (* -1 (/ (- (* -512/27 (/ (pow x 2) y)) (* 64/9 x)) y))) y))>
#<alt (* -1 (/ (+ 8/3 (* -1 (/ (- (* -1 (/ (- (* 4096/81 (/ (pow x 3) y)) (* -512/27 (pow x 2))) y)) (* 64/9 x)) y))) y))>
#<alt (* -3/8 y)>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt x>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt x>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (* -3/8 y)>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* -3/8 y)>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt x>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (* -3/8 y)>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* -3/8 y)>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -3/8 y)>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt x>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -1 (pow x 2))>
#<alt (- (* 9/64 (pow y 2)) (pow x 2))>
#<alt (- (* 9/64 (pow y 2)) (pow x 2))>
#<alt (- (* 9/64 (pow y 2)) (pow x 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))>
#<alt (* 9/64 (pow y 2))>
#<alt (* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))>
#<alt (* 9/64 (pow y 2))>
#<alt (+ (* -1 (pow x 2)) (* 9/64 (pow y 2)))>
#<alt (+ (* -1 (pow x 2)) (* 9/64 (pow y 2)))>
#<alt (+ (* -1 (pow x 2)) (* 9/64 (pow y 2)))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))>
#<alt (* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))>
#<alt (* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))>
#<alt (* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))>
#<alt (* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* -1 x)>
#<alt (- (* -3/8 y) x)>
#<alt (- (* -3/8 y) x)>
#<alt (- (* -3/8 y) x)>
#<alt (* -3/8 y)>
#<alt (* y (- (* -1 (/ x y)) 3/8))>
#<alt (* y (- (* -1 (/ x y)) 3/8))>
#<alt (* y (- (* -1 (/ x y)) 3/8))>
#<alt (* -3/8 y)>
#<alt (* -1 (* y (+ 3/8 (/ x y))))>
#<alt (* -1 (* y (+ 3/8 (/ x y))))>
#<alt (* -1 (* y (+ 3/8 (/ x y))))>
#<alt (* -3/8 y)>
#<alt (+ (* -1 x) (* -3/8 y))>
#<alt (+ (* -1 x) (* -3/8 y))>
#<alt (+ (* -1 x) (* -3/8 y))>
#<alt (* -1 x)>
#<alt (* x (- (* -3/8 (/ y x)) 1))>
#<alt (* x (- (* -3/8 (/ y x)) 1))>
#<alt (* x (- (* -3/8 (/ y x)) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 3/8 (/ y x)))))>
#<alt (* -1 (* x (+ 1 (* 3/8 (/ y x)))))>
#<alt (* -1 (* x (+ 1 (* 3/8 (/ y x)))))>

Calls

54 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	(* y 9/64)
1.0ms	y	@	0	(/ (- (* y (* y 9/64)) (* x x)) (- (* y -3/8) x))
1.0ms	x	@	0	(/ (- (* y (* y 9/64)) (* x x)) (- (* y -3/8) x))
1.0ms	y	@	inf	(/ (- (* y (* y 9/64)) (* x x)) (- (* y -3/8) x))
0.0ms	x	@	inf	(/ (- (* y (* y 9/64)) (* x x)) (- (* y -3/8) x))

rewrite436.0ms (5.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3562×	`-lowering-.f32`
3562×	`-lowering-.f64`
3198×	`/-lowering-/.f32`
3198×	`/-lowering-/.f64`
1996×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	46
1	105	44
2	901	44
0	8566	44

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 1173

Calls

Call 1

Inputs
(+ (* y -3/8) x)
(* -3/8 y)
(/ 1 (/ 1 (+ x (* y -3/8))))
(/ 1 (+ x (* y -3/8)))
(+ x (* y -3/8))
(* y -3/8)
(/ (- (* y (* y 9/64)) (* x x)) (- (* y -3/8) x))
(- (* y (* y 9/64)) (* x x))
(* y (* y 9/64))
(* y 9/64)
(- (* y -3/8) x)

Outputs
(+.f64 (*.f64 y #s(literal -3/8 binary64)) x)
(+.f64 x (*.f64 y #s(literal -3/8 binary64)))
(+.f64 x (neg.f64 (*.f64 y #s(literal 3/8 binary64))))
(+.f64 x (.f64 #s(literal -1 binary64) (.f64 y #s(literal 3/8 binary64))))
(+.f64 (+.f64 (.f64 y #s(literal -3/8 binary64)) x) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x))))
(+.f64 (+.f64 (.f64 y #s(literal -3/8 binary64)) x) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))))
(+.f64 (+.f64 (.f64 y #s(literal -3/8 binary64)) x) (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x))))
(+.f64 (+.f64 (.f64 y #s(literal -3/8 binary64)) x) (.f64 (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x))))
(+.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (/.f64 (.f64 x x) (+.f64 x (*.f64 y #s(literal 3/8 binary64)))))
(+.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (+.f64 x (.f64 y #s(literal 3/8 binary64))))))
(+.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))))
(+.f64 (/.f64 (.f64 x x) (+.f64 x (.f64 y #s(literal 3/8 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x)))
(+.f64 (fma.f64 y (/.f64 (.f64 y #s(literal 9/64 binary64)) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (neg.f64 (.f64 (/.f64 x (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) x))) (fma.f64 (neg.f64 (/.f64 x (-.f64 (.f64 y #s(literal -3/8 binary64)) x))) x (.f64 (/.f64 x (-.f64 (*.f64 y #s(literal -3/8 binary64)) x)) x)))
(+.f64 (fma.f64 y (/.f64 (.f64 y #s(literal 9/64 binary64)) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (.f64 x x)))) (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (.f64 y #s(literal 3/8 binary64)))) (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (.f64 x x))))
(+.f64 (fma.f64 y (/.f64 (.f64 y #s(literal 9/64 binary64)) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (neg.f64 (.f64 (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x (+.f64 (.f64 y #s(literal -3/8 binary64)) x))) (/.f64 (.f64 x x) (-.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64)) (.f64 x (.f64 x x))))))) (fma.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x (+.f64 (.f64 y #s(literal -3/8 binary64)) x)))) (/.f64 (.f64 x x) (-.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64)) (.f64 x (.f64 x x)))) (.f64 (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x (+.f64 (.f64 y #s(literal -3/8 binary64)) x))) (/.f64 (.f64 x x) (-.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64)) (.f64 x (.f64 x x)))))))
(+.f64 (fma.f64 y (/.f64 (.f64 y #s(literal 9/64 binary64)) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (neg.f64 (.f64 (+.f64 (.f64 y #s(literal -3/8 binary64)) x) (/.f64 (.f64 x x) (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x)))))) (fma.f64 (-.f64 (.f64 y #s(literal 3/8 binary64)) x) (/.f64 (.f64 x x) (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x))) (.f64 (+.f64 (.f64 y #s(literal -3/8 binary64)) x) (/.f64 (.f64 x x) (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x))))))
(+.f64 (fma.f64 (.f64 y #s(literal 9/64 binary64)) (/.f64 y (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (neg.f64 (.f64 (/.f64 x (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) x))) (fma.f64 (neg.f64 (/.f64 x (-.f64 (.f64 y #s(literal -3/8 binary64)) x))) x (.f64 (/.f64 x (-.f64 (*.f64 y #s(literal -3/8 binary64)) x)) x)))
(+.f64 (fma.f64 (.f64 y #s(literal 9/64 binary64)) (/.f64 y (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (.f64 x x)))) (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (.f64 y #s(literal 3/8 binary64)))) (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (.f64 x x))))
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(.f64 (/.f64 (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) #s(literal 81/4096 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x))))) (+.f64 (.f64 y #s(literal -3/8 binary64)) x)))
(.f64 (/.f64 (-.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) #s(literal 81/4096 binary64))) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x))) (+.f64 (.f64 y #s(literal -3/8 binary64)) x)))
(.f64 (/.f64 (+.f64 (.f64 y #s(literal -3/8 binary64)) x) (+.f64 (.f64 y #s(literal -3/8 binary64)) x)) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))
(.f64 (/.f64 (+.f64 (.f64 y #s(literal -3/8 binary64)) x) (+.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64)) (.f64 x (.f64 x x)))) (/.f64 (-.f64 (.f64 y #s(literal -3/8 binary64)) x) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal -3/8 binary64)) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))))))
(.f64 (/.f64 (+.f64 (.f64 y #s(literal -3/8 binary64)) x) (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64)))) (/.f64 (-.f64 (.f64 y #s(literal -3/8 binary64)) x) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y #s(literal 3/8 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 y #s(literal -3/8 binary64)) x) (pow.f64 (+.f64 (.f64 y #s(literal -3/8 binary64)) x) #s(literal 1/2 binary64))) (/.f64 (-.f64 (.f64 y #s(literal -3/8 binary64)) x) (pow.f64 (+.f64 (*.f64 y #s(literal -3/8 binary64)) x) #s(literal 1/2 binary64))))
(.f64 (/.f64 (+.f64 (.f64 y #s(literal -3/8 binary64)) x) (/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x)) (-.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64)) (.f64 x (.f64 x x))))) (/.f64 (-.f64 (.f64 y #s(literal -3/8 binary64)) x) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x (+.f64 (*.f64 y #s(literal -3/8 binary64)) x)))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 (.f64 y #s(literal -3/8 binary64)) x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) #s(literal 81/4096 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x))))) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) #s(literal 81/4096 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x))))) (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) #s(literal 81/4096 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y #s(literal 3/8 binary64))))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (pow.f64 (+.f64 (.f64 y #s(literal -3/8 binary64)) x) #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) #s(literal 81/4096 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x))))) (pow.f64 (+.f64 (*.f64 y #s(literal -3/8 binary64)) x) #s(literal 1/2 binary64))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x)) (-.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64)) (.f64 x (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) #s(literal 81/4096 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x))))) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x (+.f64 (*.f64 y #s(literal -3/8 binary64)) x)))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) #s(literal 81/4096 binary64))) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (.f64 y #s(literal -3/8 binary64)) x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x))) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) #s(literal 81/4096 binary64))) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64)) (.f64 x (.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal -3/8 binary64)) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) #s(literal 81/4096 binary64))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x))) (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) #s(literal 81/4096 binary64))) (.f64 (.f64 x x) (.f64 x x))) (pow.f64 (+.f64 (.f64 y #s(literal -3/8 binary64)) x) #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x))) (pow.f64 (+.f64 (*.f64 y #s(literal -3/8 binary64)) x) #s(literal 1/2 binary64))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) #s(literal 81/4096 binary64))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x)) (-.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -27/512 binary64)) (.f64 x (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x))) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x (+.f64 (*.f64 y #s(literal -3/8 binary64)) x)))))

simplify244.0ms (3%)

Algorithm

1×	egg-herbie

Rules

3962×	`-lowering-.f32`
3962×	`-lowering-.f64`
1372×	`/-lowering-/.f32`
1372×	`/-lowering-/.f64`
1074×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	1207
1	581	1039
2	1630	1008
3	5221	1008
0	8354	1008

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

Inputs
x
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(* -3/8 y)
(* y (- (/ x y) 3/8))
(* y (- (/ x y) 3/8))
(* y (- (/ x y) 3/8))
(* -3/8 y)
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -3/8 y)
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(+ x (* -3/8 y))
x
(* x (+ 1 (* -3/8 (/ y x))))
(* x (+ 1 (* -3/8 (/ y x))))
(* x (+ 1 (* -3/8 (/ y x))))
x
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(+ x (* -3/8 y))
x
(* x (+ 1 (* -3/8 (/ y x))))
(* x (+ 1 (* -3/8 (/ y x))))
(* x (+ 1 (* -3/8 (/ y x))))
x
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
x
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(* -3/8 y)
(* y (- (/ x y) 3/8))
(* y (- (/ x y) 3/8))
(* y (- (/ x y) 3/8))
(* -3/8 y)
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(/ -8/3 y)
(- (* -64/9 (/ x (pow y 2))) (* 8/3 (/ 1 y)))
(- (* x (- (* -512/27 (/ x (pow y 3))) (* 64/9 (/ 1 (pow y 2))))) (* 8/3 (/ 1 y)))
(- (* x (- (* x (- (* -4096/81 (/ x (pow y 4))) (* 512/27 (/ 1 (pow y 3))))) (* 64/9 (/ 1 (pow y 2))))) (* 8/3 (/ 1 y)))
(/ 1 x)
(/ (+ 1 (* 3/8 (/ y x))) x)
(/ (- (+ 1 (* 9/64 (/ (pow y 2) (pow x 2)))) (* -3/8 (/ y x))) x)
(/ (- (+ 1 (* 27/512 (/ (pow y 3) (pow x 3)))) (+ (* -3/8 (/ y x)) (* -9/64 (/ (pow y 2) (pow x 2))))) x)
(/ 1 x)
(* -1 (/ (- (* -3/8 (/ y x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* 9/64 (/ (pow y 2) x)) (* -3/8 y)) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -27/512 (/ (pow y 3) x)) (* 9/64 (pow y 2))) x)) (* -3/8 y)) x)) 1) x))
(/ 1 x)
(+ (* 3/8 (/ y (pow x 2))) (/ 1 x))
(+ (* y (+ (* 9/64 (/ y (pow x 3))) (* 3/8 (/ 1 (pow x 2))))) (/ 1 x))
(+ (* y (+ (* y (+ (* 27/512 (/ y (pow x 4))) (* 9/64 (/ 1 (pow x 3))))) (* 3/8 (/ 1 (pow x 2))))) (/ 1 x))
(/ -8/3 y)
(/ (- (* -64/9 (/ x y)) 8/3) y)
(/ (- (* -512/27 (/ (pow x 2) (pow y 2))) (+ 8/3 (* 64/9 (/ x y)))) y)
(/ (- (* -4096/81 (/ (pow x 3) (pow y 3))) (+ 8/3 (+ (* 64/9 (/ x y)) (* 512/27 (/ (pow x 2) (pow y 2)))))) y)
(/ -8/3 y)
(* -1 (/ (+ 8/3 (* 64/9 (/ x y))) y))
(* -1 (/ (+ 8/3 (* -1 (/ (- (* -512/27 (/ (pow x 2) y)) (* 64/9 x)) y))) y))
(* -1 (/ (+ 8/3 (* -1 (/ (- (* -1 (/ (- (* 4096/81 (/ (pow x 3) y)) (* -512/27 (pow x 2))) y)) (* 64/9 x)) y))) y))
(* -3/8 y)
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(+ x (* -3/8 y))
x
(* x (+ 1 (* -3/8 (/ y x))))
(* x (+ 1 (* -3/8 (/ y x))))
(* x (+ 1 (* -3/8 (/ y x))))
x
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
x
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(* -3/8 y)
(* y (- (/ x y) 3/8))
(* y (- (/ x y) 3/8))
(* y (- (/ x y) 3/8))
(* -3/8 y)
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
x
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(* -3/8 y)
(* y (- (/ x y) 3/8))
(* y (- (/ x y) 3/8))
(* y (- (/ x y) 3/8))
(* -3/8 y)
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -3/8 y)
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(+ x (* -3/8 y))
x
(* x (+ 1 (* -3/8 (/ y x))))
(* x (+ 1 (* -3/8 (/ y x))))
(* x (+ 1 (* -3/8 (/ y x))))
x
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -1 (pow x 2))
(- (* 9/64 (pow y 2)) (pow x 2))
(- (* 9/64 (pow y 2)) (pow x 2))
(- (* 9/64 (pow y 2)) (pow x 2))
(* 9/64 (pow y 2))
(* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))
(* 9/64 (pow y 2))
(* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))
(* 9/64 (pow y 2))
(+ (* -1 (pow x 2)) (* 9/64 (pow y 2)))
(+ (* -1 (pow x 2)) (* 9/64 (pow y 2)))
(+ (* -1 (pow x 2)) (* 9/64 (pow y 2)))
(* -1 (pow x 2))
(* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))
(* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))
(* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))
(* -1 (pow x 2))
(* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))
(* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))
(* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* -1 x)
(- (* -3/8 y) x)
(- (* -3/8 y) x)
(- (* -3/8 y) x)
(* -3/8 y)
(* y (- (* -1 (/ x y)) 3/8))
(* y (- (* -1 (/ x y)) 3/8))
(* y (- (* -1 (/ x y)) 3/8))
(* -3/8 y)
(* -1 (* y (+ 3/8 (/ x y))))
(* -1 (* y (+ 3/8 (/ x y))))
(* -1 (* y (+ 3/8 (/ x y))))
(* -3/8 y)
(+ (* -1 x) (* -3/8 y))
(+ (* -1 x) (* -3/8 y))
(+ (* -1 x) (* -3/8 y))
(* -1 x)
(* x (- (* -3/8 (/ y x)) 1))
(* x (- (* -3/8 (/ y x)) 1))
(* x (- (* -3/8 (/ y x)) 1))
(* -1 x)
(* -1 (* x (+ 1 (* 3/8 (/ y x)))))
(* -1 (* x (+ 1 (* 3/8 (/ y x)))))
(* -1 (* x (+ 1 (* 3/8 (/ y x)))))

Outputs
x
(+ x (* -3/8 y))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(+ x (* -3/8 y))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(+ x (* -3/8 y))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* y (- (/ x y) 3/8))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* y (- (/ x y) 3/8))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* y (- (/ x y) 3/8))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(+ x (* -3/8 y))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(+ x (* -3/8 y))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(+ x (* -3/8 y))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
x
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
x
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(+ x (* -3/8 y))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(+ x (* -3/8 y))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(+ x (* -3/8 y))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
x
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
x
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
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(* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))
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(* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))
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(* -1 (pow x 2))
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(* 9/64 y)
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(* 9/64 y)
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(* 9/64 y)
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(* 9/64 y)
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(* 9/64 y)
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(* 9/64 y)
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(* 9/64 y)
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(* 9/64 y)
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(*.f64 #s(literal -3/8 binary64) y)
(* y (- (* -1 (/ x y)) 3/8))
(-.f64 (*.f64 #s(literal -3/8 binary64) y) x)
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(-.f64 (*.f64 #s(literal -3/8 binary64) y) x)
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(-.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -1 (* y (+ 3/8 (/ x y))))
(-.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(* -1 (* y (+ 3/8 (/ x y))))
(-.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(* -1 (* y (+ 3/8 (/ x y))))
(-.f64 (*.f64 #s(literal -3/8 binary64) y) x)
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(*.f64 #s(literal -3/8 binary64) y)
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(* x (- (* -3/8 (/ y x)) 1))
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(-.f64 (*.f64 #s(literal -3/8 binary64) y) x)
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(-.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(* -1 (* x (+ 1 (* 3/8 (/ y x)))))
(-.f64 (*.f64 #s(literal -3/8 binary64) y) x)

eval251.0ms (3.1%)

Compiler: Compiled 51600 to 2159 computations (95.8% saved)

prune118.0ms (1.4%)

Pruning

11 alts after pruning (6 fresh and 5 done)

	Pruned	Kept	Total
New	1400	5	1405
Fresh	1	1	2
Picked	1	4	5
Done	0	1	1
Total	1402	11	1413

Accuracy

100.0%

Counts

1413 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 y #s(literal -3/8 binary64) x)
	28.5%	(/.f64 (/.f64 (-.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) #s(literal 81/4096 binary64))) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x)))
✓	57.9%	(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x)) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))
▶	31.9%	(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x)) (.f64 #s(literal -3/8 binary64) y))
▶	32.1%	(/.f64 (.f64 (.f64 y y) #s(literal 9/64 binary64)) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x))
▶	52.4%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -8/3 binary64) (*.f64 (/.f64 x y) #s(literal -64/9 binary64))) y))
▶	52.0%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -8/3 binary64) y))
✓	99.9%	(+.f64 x (*.f64 y #s(literal -3/8 binary64)))
▶	99.6%	(.f64 (+.f64 x (.f64 y #s(literal -3/8 binary64))) (.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y #s(literal -3/8 binary64))))))
✓	52.1%	(*.f64 #s(literal -3/8 binary64) y)
✓	48.8%	x

Compiler

Compiled 246 to 152 computations (38.2% saved)

simplify202.0ms (2.5%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 y #s(literal 9/64 binary64))
✓	cost-diff	0	(.f64 y (.f64 y #s(literal 9/64 binary64)))
✓	cost-diff	0	(-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x))
✓	cost-diff	128	(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x)) (.f64 #s(literal -3/8 binary64) y))
✓	cost-diff	0	(-.f64 (*.f64 y #s(literal -3/8 binary64)) x)
✓	cost-diff	0	(*.f64 y y)
✓	cost-diff	0	(.f64 (.f64 y y) #s(literal 9/64 binary64))
✓	cost-diff	0	(/.f64 (.f64 (.f64 y y) #s(literal 9/64 binary64)) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x))
✓	cost-diff	0	(*.f64 (/.f64 x y) #s(literal -64/9 binary64))
✓	cost-diff	0	(+.f64 #s(literal -8/3 binary64) (*.f64 (/.f64 x y) #s(literal -64/9 binary64)))
✓	cost-diff	0	(/.f64 (+.f64 #s(literal -8/3 binary64) (*.f64 (/.f64 x y) #s(literal -64/9 binary64))) y)
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -8/3 binary64) (*.f64 (/.f64 x y) #s(literal -64/9 binary64))) y))
✓	cost-diff	0	(/.f64 #s(literal -8/3 binary64) y)
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -8/3 binary64) y))
✓	cost-diff	0	(*.f64 y #s(literal -3/8 binary64))
✓	cost-diff	0	(+.f64 x (*.f64 y #s(literal -3/8 binary64)))
✓	cost-diff	768	(.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y #s(literal -3/8 binary64)))))
✓	cost-diff	896	(.f64 (+.f64 x (.f64 y #s(literal -3/8 binary64))) (.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y #s(literal -3/8 binary64))))))

Rules

4292×	`-lowering-.f32`
4292×	`-lowering-.f64`
1544×	`sum4-define`
1504×	`/-lowering-/.f32`
1504×	`/-lowering-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	141
1	81	130
2	205	126
3	596	126
4	3366	126
0	8485	126

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (+ x (* y -3/8)) (* (- x (* y -3/8)) (/ 1 (- x (* y -3/8)))))
(+ x (* y -3/8))
x
(* y -3/8)
y
-3/8
(* (- x (* y -3/8)) (/ 1 (- x (* y -3/8))))
(- x (* y -3/8))
(/ 1 (- x (* y -3/8)))
1
(/ 1 (/ -8/3 y))
1
(/ -8/3 y)
-8/3
y
(/ 1 (/ (+ -8/3 (* (/ x y) -64/9)) y))
1
(/ (+ -8/3 (* (/ x y) -64/9)) y)
(+ -8/3 (* (/ x y) -64/9))
-8/3
(* (/ x y) -64/9)
(/ x y)
x
y
-64/9
(/ (* (* y y) 9/64) (- (* y -3/8) x))
(* (* y y) 9/64)
(* y y)
y
9/64
(- (* y -3/8) x)
(* y -3/8)
-3/8
x
(/ (- (* y (* y 9/64)) (* x x)) (* -3/8 y))
(- (* y (* y 9/64)) (* x x))
(* y (* y 9/64))
y
(* y 9/64)
9/64
(* x x)
x
(* -3/8 y)
-3/8

Outputs
(* (+ x (* y -3/8)) (* (- x (* y -3/8)) (/ 1 (- x (* y -3/8)))))
(+.f64 x (*.f64 y #s(literal -3/8 binary64)))
(+ x (* y -3/8))
(+.f64 x (*.f64 y #s(literal -3/8 binary64)))
x
(* y -3/8)
(*.f64 y #s(literal -3/8 binary64))
y
-3/8
#s(literal -3/8 binary64)
(* (- x (* y -3/8)) (/ 1 (- x (* y -3/8))))
#s(literal 1 binary64)
(- x (* y -3/8))
(+.f64 x (*.f64 y #s(literal 3/8 binary64)))
(/ 1 (- x (* y -3/8)))
(/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y #s(literal 3/8 binary64))))
1
#s(literal 1 binary64)
(/ 1 (/ -8/3 y))
(*.f64 y #s(literal -3/8 binary64))
1
#s(literal 1 binary64)
(/ -8/3 y)
(/.f64 #s(literal -8/3 binary64) y)
-8/3
#s(literal -8/3 binary64)
y
(/ 1 (/ (+ -8/3 (* (/ x y) -64/9)) y))
(/.f64 y (+.f64 #s(literal -8/3 binary64) (*.f64 x (/.f64 #s(literal -64/9 binary64) y))))
1
#s(literal 1 binary64)
(/ (+ -8/3 (* (/ x y) -64/9)) y)
(/.f64 (+.f64 #s(literal -8/3 binary64) (*.f64 x (/.f64 #s(literal -64/9 binary64) y))) y)
(+ -8/3 (* (/ x y) -64/9))
(+.f64 #s(literal -8/3 binary64) (*.f64 x (/.f64 #s(literal -64/9 binary64) y)))
-8/3
#s(literal -8/3 binary64)
(* (/ x y) -64/9)
(*.f64 x (/.f64 #s(literal -64/9 binary64) y))
(/ x y)
(/.f64 x y)
x
y
-64/9
#s(literal -64/9 binary64)
(/ (* (* y y) 9/64) (- (* y -3/8) x))
(.f64 y (.f64 #s(literal 9/64 binary64) (/.f64 y (-.f64 (*.f64 y #s(literal -3/8 binary64)) x))))
(* (* y y) 9/64)
(.f64 y (.f64 y #s(literal 9/64 binary64)))
(* y y)
(*.f64 y y)
y
9/64
#s(literal 9/64 binary64)
(- (* y -3/8) x)
(-.f64 (*.f64 y #s(literal -3/8 binary64)) x)
(* y -3/8)
(*.f64 y #s(literal -3/8 binary64))
-3/8
#s(literal -3/8 binary64)
x
(/ (- (* y (* y 9/64)) (* x x)) (* -3/8 y))
(+.f64 (.f64 y #s(literal -3/8 binary64)) (/.f64 (/.f64 (.f64 x x) y) #s(literal 3/8 binary64)))
(- (* y (* y 9/64)) (* x x))
(-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x))
(* y (* y 9/64))
(.f64 y (.f64 y #s(literal 9/64 binary64)))
y
(* y 9/64)
(*.f64 y #s(literal 9/64 binary64))
9/64
#s(literal 9/64 binary64)
(* x x)
(*.f64 x x)
x
(* -3/8 y)
(*.f64 y #s(literal -3/8 binary64))
-3/8
#s(literal -3/8 binary64)

localize391.0ms (4.8%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal -3/8 binary64) y)
✓	accuracy	99.8%	(.f64 y (.f64 y #s(literal 9/64 binary64)))
✓	accuracy	98.7%	(-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x))
✓	accuracy	83.6%	(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x)) (.f64 #s(literal -3/8 binary64) y))
✓	accuracy	100.0%	(*.f64 y y)
✓	accuracy	100.0%	(*.f64 y #s(literal -3/8 binary64))
✓	accuracy	99.8%	(.f64 (.f64 y y) #s(literal 9/64 binary64))
✓	accuracy	84.3%	(/.f64 (.f64 (.f64 y y) #s(literal 9/64 binary64)) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x))
✓	accuracy	100.0%	(+.f64 #s(literal -8/3 binary64) (*.f64 (/.f64 x y) #s(literal -64/9 binary64)))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -8/3 binary64) (*.f64 (/.f64 x y) #s(literal -64/9 binary64))) y))
✓	accuracy	99.8%	(/.f64 (+.f64 #s(literal -8/3 binary64) (*.f64 (/.f64 x y) #s(literal -64/9 binary64))) y)
✓	accuracy	99.7%	(*.f64 (/.f64 x y) #s(literal -64/9 binary64))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -8/3 binary64) y))
✓	accuracy	99.6%	(/.f64 #s(literal -8/3 binary64) y)
✓	accuracy	100.0%	(.f64 (+.f64 x (.f64 y #s(literal -3/8 binary64))) (.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y #s(literal -3/8 binary64))))))
✓	accuracy	100.0%	(*.f64 y #s(literal -3/8 binary64))
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y #s(literal -3/8 binary64))))
✓	accuracy	99.8%	(.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y #s(literal -3/8 binary64)))))

Results

263.0ms	83×	5	exit
64.0ms	173×	0	valid

Compiler

Compiled 181 to 31 computations (82.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 229.0ms

ival-div: 106.0ms (46.4% of total)

ival-mult: 51.0ms (22.3% of total)

...c/correct-round.rkt:119:19: 31.0ms (13.6% of total)

backward-pass: 26.0ms (11.4% of total)

ival-sub: 8.0ms (3.5% of total)

ival-add: 6.0ms (2.6% of total)

const: 1.0ms (0.4% of total)

series34.0ms (0.4%)

Counts

20 → 384

Calls

Call 1

Inputs
#<alt (* (+ x (* y -3/8)) (* (- x (* y -3/8)) (/ 1 (- x (* y -3/8)))))>
#<alt (* (- x (* y -3/8)) (/ 1 (- x (* y -3/8))))>
#<alt (+ x (* y -3/8))>
#<alt (* y -3/8)>
#<alt (/ 1 (/ -8/3 y))>
#<alt (/ -8/3 y)>
#<alt (/ 1 (/ (+ -8/3 (* (/ x y) -64/9)) y))>
#<alt (/ (+ -8/3 (* (/ x y) -64/9)) y)>
#<alt (+ -8/3 (* (/ x y) -64/9))>
#<alt (* (/ x y) -64/9)>
#<alt (/ (* (* y y) 9/64) (- (* y -3/8) x))>
#<alt (* (* y y) 9/64)>
#<alt (* y y)>
#<alt (- (* y -3/8) x)>
#<alt (/ (- (* y (* y 9/64)) (* x x)) (* -3/8 y))>
#<alt (- (* y (* y 9/64)) (* x x))>
#<alt (* y (* y 9/64))>
#<alt (* y 9/64)>
#<alt (/ 1 (- x (* y -3/8)))>
#<alt (* -3/8 y)>

Outputs
#<alt (* -3/8 y)>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt x>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt x>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (* -3/8 y)>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* -3/8 y)>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt (* -3/8 y)>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt x>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt x>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (* -3/8 y)>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* -3/8 y)>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (* -3/8 y)>
#<alt (+ x (* -3/8 y))>
#<alt (+ (* -3/8 y) (* x (+ 1 (* -8/3 (/ x y)))))>
#<alt (+ (* -3/8 y) (* x (+ 1 (* x (- (* 64/9 (/ x (pow y 2))) (* 8/3 (/ 1 y)))))))>
#<alt (* -9/64 (/ (pow y 2) x))>
#<alt (/ (+ (* -9/64 (pow y 2)) (* 27/512 (/ (pow y 3) x))) x)>
#<alt (/ (+ (* -9/64 (pow y 2)) (+ (* -81/4096 (/ (pow y 4) (pow x 2))) (* 27/512 (/ (pow y 3) x)))) x)>
#<alt (/ (+ (* -9/64 (pow y 2)) (+ (* -81/4096 (/ (pow y 4) (pow x 2))) (+ (* 243/32768 (/ (pow y 5) (pow x 3))) (* 27/512 (/ (pow y 3) x))))) x)>
#<alt (* -9/64 (/ (pow y 2) x))>
#<alt (* -1 (/ (+ (* -27/512 (/ (pow y 3) x)) (* 9/64 (pow y 2))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -81/4096 (/ (pow y 4) x)) (* -27/512 (pow y 3))) x)) (* 9/64 (pow y 2))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* -243/32768 (/ (pow y 5) x)) (* -81/4096 (pow y 4))) x)) (* -27/512 (pow y 3))) x)) (* 9/64 (pow y 2))) x))>
#<alt (* -9/64 (/ (pow y 2) x))>
#<alt (* (pow y 2) (- (* 27/512 (/ y (pow x 2))) (* 9/64 (/ 1 x))))>
#<alt (* (pow y 2) (- (* y (+ (* -81/4096 (/ y (pow x 3))) (* 27/512 (/ 1 (pow x 2))))) (* 9/64 (/ 1 x))))>
#<alt (* (pow y 2) (- (* y (+ (* y (- (* 243/32768 (/ y (pow x 4))) (* 81/4096 (/ 1 (pow x 3))))) (* 27/512 (/ 1 (pow x 2))))) (* 9/64 (/ 1 x))))>
#<alt (* -3/8 y)>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (* -8/3 (/ (pow x 2) (pow y 2))) (+ 3/8 (* -1 (/ x y)))))>
#<alt (* y (- (* 64/9 (/ (pow x 3) (pow y 3))) (+ 3/8 (+ (* -1 (/ x y)) (* 8/3 (/ (pow x 2) (pow y 2)))))))>
#<alt (* -3/8 y)>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ (- (* -8/3 (/ (pow x 2) y)) (* -1 x)) y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ (- (* -1 (/ (- (* -64/9 (/ (pow x 3) y)) (* -8/3 (pow x 2))) y)) (* -1 x)) y)))))>
#<alt (/ -8/3 y)>
#<alt (- (* -64/9 (/ x (pow y 2))) (* 8/3 (/ 1 y)))>
#<alt (- (* -64/9 (/ x (pow y 2))) (* 8/3 (/ 1 y)))>
#<alt (- (* -64/9 (/ x (pow y 2))) (* 8/3 (/ 1 y)))>
#<alt (* -64/9 (/ x (pow y 2)))>
#<alt (* -1 (* x (+ (* 8/3 (/ 1 (* x y))) (* 64/9 (/ 1 (pow y 2))))))>
#<alt (* -1 (* x (+ (* 8/3 (/ 1 (* x y))) (* 64/9 (/ 1 (pow y 2))))))>
#<alt (* -1 (* x (+ (* 8/3 (/ 1 (* x y))) (* 64/9 (/ 1 (pow y 2))))))>
#<alt (* -64/9 (/ x (pow y 2)))>
#<alt (* -1 (* x (+ (* 8/3 (/ 1 (* x y))) (* 64/9 (/ 1 (pow y 2))))))>
#<alt (* -1 (* x (+ (* 8/3 (/ 1 (* x y))) (* 64/9 (/ 1 (pow y 2))))))>
#<alt (* -1 (* x (+ (* 8/3 (/ 1 (* x y))) (* 64/9 (/ 1 (pow y 2))))))>
#<alt (* -64/9 (/ x (pow y 2)))>
#<alt (/ (+ (* -64/9 x) (* -8/3 y)) (pow y 2))>
#<alt (/ (+ (* -64/9 x) (* -8/3 y)) (pow y 2))>
#<alt (/ (+ (* -64/9 x) (* -8/3 y)) (pow y 2))>
#<alt (/ -8/3 y)>
#<alt (/ (- (* -64/9 (/ x y)) 8/3) y)>
#<alt (/ (- (* -64/9 (/ x y)) 8/3) y)>
#<alt (/ (- (* -64/9 (/ x y)) 8/3) y)>
#<alt (/ -8/3 y)>
#<alt (* -1 (/ (+ 8/3 (* 64/9 (/ x y))) y))>
#<alt (* -1 (/ (+ 8/3 (* 64/9 (/ x y))) y))>
#<alt (* -1 (/ (+ 8/3 (* 64/9 (/ x y))) y))>
#<alt -8/3>
#<alt (- (* -64/9 (/ x y)) 8/3)>
#<alt (- (* -64/9 (/ x y)) 8/3)>
#<alt (- (* -64/9 (/ x y)) 8/3)>
#<alt (* -64/9 (/ x y))>
#<alt (* -1 (* x (+ (* 64/9 (/ 1 y)) (* 8/3 (/ 1 x)))))>
#<alt (* -1 (* x (+ (* 64/9 (/ 1 y)) (* 8/3 (/ 1 x)))))>
#<alt (* -1 (* x (+ (* 64/9 (/ 1 y)) (* 8/3 (/ 1 x)))))>
#<alt (* -64/9 (/ x y))>
#<alt (* -1 (* x (+ (* 8/3 (/ 1 x)) (* 64/9 (/ 1 y)))))>
#<alt (* -1 (* x (+ (* 8/3 (/ 1 x)) (* 64/9 (/ 1 y)))))>
#<alt (* -1 (* x (+ (* 8/3 (/ 1 x)) (* 64/9 (/ 1 y)))))>
#<alt (* -64/9 (/ x y))>
#<alt (/ (+ (* -64/9 x) (* -8/3 y)) y)>
#<alt (/ (+ (* -64/9 x) (* -8/3 y)) y)>
#<alt (/ (+ (* -64/9 x) (* -8/3 y)) y)>
#<alt -8/3>
#<alt (- (* -64/9 (/ x y)) 8/3)>
#<alt (- (* -64/9 (/ x y)) 8/3)>
#<alt (- (* -64/9 (/ x y)) 8/3)>
#<alt -8/3>
#<alt (- (* -64/9 (/ x y)) 8/3)>
#<alt (- (* -64/9 (/ x y)) 8/3)>
#<alt (- (* -64/9 (/ x y)) 8/3)>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -64/9 (/ x y))>
#<alt (* -9/64 (/ (pow y 2) x))>
#<alt (* (pow y 2) (- (* 27/512 (/ y (pow x 2))) (* 9/64 (/ 1 x))))>
#<alt (* (pow y 2) (- (* y (+ (* -81/4096 (/ y (pow x 3))) (* 27/512 (/ 1 (pow x 2))))) (* 9/64 (/ 1 x))))>
#<alt (* (pow y 2) (- (* y (+ (* y (- (* 243/32768 (/ y (pow x 4))) (* 81/4096 (/ 1 (pow x 3))))) (* 27/512 (/ 1 (pow x 2))))) (* 9/64 (/ 1 x))))>
#<alt (* -3/8 y)>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (* -8/3 (/ (pow x 2) (pow y 2))) (+ 3/8 (* -1 (/ x y)))))>
#<alt (* y (- (* 64/9 (/ (pow x 3) (pow y 3))) (+ 3/8 (+ (* -1 (/ x y)) (* 8/3 (/ (pow x 2) (pow y 2)))))))>
#<alt (* -3/8 y)>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ (- (* -8/3 (/ (pow x 2) y)) (* -1 x)) y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ (- (* -1 (/ (- (* -64/9 (/ (pow x 3) y)) (* -8/3 (pow x 2))) y)) (* -1 x)) y)))))>
#<alt (* -3/8 y)>
#<alt (+ x (* -3/8 y))>
#<alt (+ (* -3/8 y) (* x (+ 1 (* -8/3 (/ x y)))))>
#<alt (+ (* -3/8 y) (* x (+ 1 (* x (- (* 64/9 (/ x (pow y 2))) (* 8/3 (/ 1 y)))))))>
#<alt (* -9/64 (/ (pow y 2) x))>
#<alt (/ (+ (* -9/64 (pow y 2)) (* 27/512 (/ (pow y 3) x))) x)>
#<alt (/ (+ (* -9/64 (pow y 2)) (+ (* -81/4096 (/ (pow y 4) (pow x 2))) (* 27/512 (/ (pow y 3) x)))) x)>
#<alt (/ (+ (* -9/64 (pow y 2)) (+ (* -81/4096 (/ (pow y 4) (pow x 2))) (+ (* 243/32768 (/ (pow y 5) (pow x 3))) (* 27/512 (/ (pow y 3) x))))) x)>
#<alt (* -9/64 (/ (pow y 2) x))>
#<alt (* -1 (/ (+ (* -27/512 (/ (pow y 3) x)) (* 9/64 (pow y 2))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -81/4096 (/ (pow y 4) x)) (* 27/512 (pow y 3))) x)) (* 9/64 (pow y 2))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -243/32768 (/ (pow y 5) x)) (* 81/4096 (pow y 4))) x)) (* 27/512 (pow y 3))) x)) (* 9/64 (pow y 2))) x))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (* -1 x)>
#<alt (- (* -3/8 y) x)>
#<alt (- (* -3/8 y) x)>
#<alt (- (* -3/8 y) x)>
#<alt (* -3/8 y)>
#<alt (* y (- (* -1 (/ x y)) 3/8))>
#<alt (* y (- (* -1 (/ x y)) 3/8))>
#<alt (* y (- (* -1 (/ x y)) 3/8))>
#<alt (* -3/8 y)>
#<alt (* -1 (* y (+ 3/8 (/ x y))))>
#<alt (* -1 (* y (+ 3/8 (/ x y))))>
#<alt (* -1 (* y (+ 3/8 (/ x y))))>
#<alt (* -3/8 y)>
#<alt (+ (* -1 x) (* -3/8 y))>
#<alt (+ (* -1 x) (* -3/8 y))>
#<alt (+ (* -1 x) (* -3/8 y))>
#<alt (* -1 x)>
#<alt (* x (- (* -3/8 (/ y x)) 1))>
#<alt (* x (- (* -3/8 (/ y x)) 1))>
#<alt (* x (- (* -3/8 (/ y x)) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 3/8 (/ y x)))))>
#<alt (* -1 (* x (+ 1 (* 3/8 (/ y x)))))>
#<alt (* -1 (* x (+ 1 (* 3/8 (/ y x)))))>
#<alt (* 8/3 (/ (pow x 2) y))>
#<alt (/ (+ (* -3/8 (pow y 2)) (* 8/3 (pow x 2))) y)>
#<alt (/ (+ (* -3/8 (pow y 2)) (* 8/3 (pow x 2))) y)>
#<alt (/ (+ (* -3/8 (pow y 2)) (* 8/3 (pow x 2))) y)>
#<alt (* -3/8 y)>
#<alt (* y (- (* 8/3 (/ (pow x 2) (pow y 2))) 3/8))>
#<alt (* y (- (* 8/3 (/ (pow x 2) (pow y 2))) 3/8))>
#<alt (* y (- (* 8/3 (/ (pow x 2) (pow y 2))) 3/8))>
#<alt (* -3/8 y)>
#<alt (* -1 (* y (+ 3/8 (* -8/3 (/ (pow x 2) (pow y 2))))))>
#<alt (* -1 (* y (+ 3/8 (* -8/3 (/ (pow x 2) (pow y 2))))))>
#<alt (* -1 (* y (+ 3/8 (* -8/3 (/ (pow x 2) (pow y 2))))))>
#<alt (* -3/8 y)>
#<alt (+ (* -3/8 y) (* 8/3 (/ (pow x 2) y)))>
#<alt (+ (* -3/8 y) (* 8/3 (/ (pow x 2) y)))>
#<alt (+ (* -3/8 y) (* 8/3 (/ (pow x 2) y)))>
#<alt (* 8/3 (/ (pow x 2) y))>
#<alt (* (pow x 2) (+ (* -3/8 (/ y (pow x 2))) (* 8/3 (/ 1 y))))>
#<alt (* (pow x 2) (+ (* -3/8 (/ y (pow x 2))) (* 8/3 (/ 1 y))))>
#<alt (* (pow x 2) (+ (* -3/8 (/ y (pow x 2))) (* 8/3 (/ 1 y))))>
#<alt (* 8/3 (/ (pow x 2) y))>
#<alt (* (pow x 2) (+ (* -3/8 (/ y (pow x 2))) (* 8/3 (/ 1 y))))>
#<alt (* (pow x 2) (+ (* -3/8 (/ y (pow x 2))) (* 8/3 (/ 1 y))))>
#<alt (* (pow x 2) (+ (* -3/8 (/ y (pow x 2))) (* 8/3 (/ 1 y))))>
#<alt (* -1 (pow x 2))>
#<alt (- (* 9/64 (pow y 2)) (pow x 2))>
#<alt (- (* 9/64 (pow y 2)) (pow x 2))>
#<alt (- (* 9/64 (pow y 2)) (pow x 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))>
#<alt (* 9/64 (pow y 2))>
#<alt (* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))>
#<alt (* 9/64 (pow y 2))>
#<alt (+ (* -1 (pow x 2)) (* 9/64 (pow y 2)))>
#<alt (+ (* -1 (pow x 2)) (* 9/64 (pow y 2)))>
#<alt (+ (* -1 (pow x 2)) (* 9/64 (pow y 2)))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))>
#<alt (* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))>
#<alt (* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))>
#<alt (* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))>
#<alt (* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 (pow y 2))>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (/ 8/3 y)>
#<alt (+ (* -64/9 (/ x (pow y 2))) (* 8/3 (/ 1 y)))>
#<alt (+ (* x (- (* 512/27 (/ x (pow y 3))) (* 64/9 (/ 1 (pow y 2))))) (* 8/3 (/ 1 y)))>
#<alt (+ (* x (- (* x (+ (* -4096/81 (/ x (pow y 4))) (* 512/27 (/ 1 (pow y 3))))) (* 64/9 (/ 1 (pow y 2))))) (* 8/3 (/ 1 y)))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -3/8 (/ y x))) x)>
#<alt (/ (- (+ 1 (* 9/64 (/ (pow y 2) (pow x 2)))) (* 3/8 (/ y x))) x)>
#<alt (/ (- (+ 1 (* -27/512 (/ (pow y 3) (pow x 3)))) (+ (* -9/64 (/ (pow y 2) (pow x 2))) (* 3/8 (/ y x)))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (* 3/8 (/ y x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 9/64 (/ (pow y 2) x)) (* 3/8 y)) x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 27/512 (/ (pow y 3) x)) (* 9/64 (pow y 2))) x)) (* 3/8 y)) x)) 1) x))>
#<alt (/ 1 x)>
#<alt (+ (* -3/8 (/ y (pow x 2))) (/ 1 x))>
#<alt (+ (* y (- (* 9/64 (/ y (pow x 3))) (* 3/8 (/ 1 (pow x 2))))) (/ 1 x))>
#<alt (+ (* y (- (* y (+ (* -27/512 (/ y (pow x 4))) (* 9/64 (/ 1 (pow x 3))))) (* 3/8 (/ 1 (pow x 2))))) (/ 1 x))>
#<alt (/ 8/3 y)>
#<alt (/ (+ 8/3 (* -64/9 (/ x y))) y)>
#<alt (/ (- (+ 8/3 (* 512/27 (/ (pow x 2) (pow y 2)))) (* 64/9 (/ x y))) y)>
#<alt (/ (- (+ 8/3 (* -4096/81 (/ (pow x 3) (pow y 3)))) (+ (* -512/27 (/ (pow x 2) (pow y 2))) (* 64/9 (/ x y)))) y)>
#<alt (/ 8/3 y)>
#<alt (* -1 (/ (- (* 64/9 (/ x y)) 8/3) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 512/27 (/ (pow x 2) y)) (* 64/9 x)) y)) 8/3) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 4096/81 (/ (pow x 3) y)) (* 512/27 (pow x 2))) y)) (* 64/9 x)) y)) 8/3) y))>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>

Calls

96 calls:

Time	Variable		Point	Expression
14.0ms	x	@	inf	(- (* y -3/8) x)
3.0ms	y	@	inf	(* (/ x y) -64/9)
1.0ms	x	@	inf	(/ (+ -8/3 (* (/ x y) -64/9)) y)
1.0ms	x	@	inf	(/ 1 (/ (+ -8/3 (* (/ x y) -64/9)) y))
1.0ms	x	@	-inf	(/ 1 (/ (+ -8/3 (* (/ x y) -64/9)) y))

rewrite394.0ms (4.8%)

Algorithm

1×	batch-egg-rewrite

Rules

2932×	`/-lowering-/.f32`
2932×	`/-lowering-/.f64`
2656×	`-lowering-.f32`
2656×	`-lowering-.f64`
2036×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	108
1	195	96
2	1577	95
0	8350	95

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 961

Calls

Call 1

Inputs
(* (+ x (* y -3/8)) (* (- x (* y -3/8)) (/ 1 (- x (* y -3/8)))))
(* (- x (* y -3/8)) (/ 1 (- x (* y -3/8))))
(+ x (* y -3/8))
(* y -3/8)
(/ 1 (/ -8/3 y))
(/ -8/3 y)
(/ 1 (/ (+ -8/3 (* (/ x y) -64/9)) y))
(/ (+ -8/3 (* (/ x y) -64/9)) y)
(+ -8/3 (* (/ x y) -64/9))
(* (/ x y) -64/9)
(/ (* (* y y) 9/64) (- (* y -3/8) x))
(* (* y y) 9/64)
(* y y)
(- (* y -3/8) x)
(/ (- (* y (* y 9/64)) (* x x)) (* -3/8 y))
(- (* y (* y 9/64)) (* x x))
(* y (* y 9/64))
(* y 9/64)
(/ 1 (- x (* y -3/8)))
(* -3/8 y)

Outputs
(+.f64 x (/.f64 y #s(literal -8/3 binary64)))
(+.f64 (/.f64 y #s(literal -8/3 binary64)) x)
(+.f64 (/.f64 y #s(literal -8/3 binary64)) (*.f64 #s(literal 1 binary64) x))
(+.f64 (/.f64 y #s(literal -8/3 binary64)) (*.f64 x #s(literal 1 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 y #s(literal -8/3 binary64)))
(+.f64 (*.f64 x #s(literal 1 binary64)) (/.f64 y #s(literal -8/3 binary64)))
(-.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)) (/.f64 (*.f64 x x) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)))
(-.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)) (/.f64 (-.f64 (.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x))) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)))
(-.f64 (/.f64 (.f64 x x) (+.f64 x (.f64 y #s(literal 3/8 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (+.f64 x (*.f64 y #s(literal 3/8 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64))) (+.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 81/4096 binary64)) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x))))) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)) (/.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 81/4096 binary64)) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x))))) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 81/4096 binary64)) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x))) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)) (/.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x))) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)))
(fma.f64 x #s(literal 1 binary64) (/.f64 y #s(literal -8/3 binary64)))
(fma.f64 y #s(literal -3/8 binary64) x)
(fma.f64 y #s(literal -3/8 binary64) (*.f64 #s(literal 1 binary64) x))
(fma.f64 y #s(literal -3/8 binary64) (*.f64 x #s(literal 1 binary64)))
(fma.f64 #s(literal -3/8 binary64) y x)
(fma.f64 #s(literal -3/8 binary64) y (*.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal -3/8 binary64) y (*.f64 x #s(literal 1 binary64)))
(fma.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1 binary64) x)
(fma.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1 binary64) (*.f64 x #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) x (/.f64 y #s(literal -8/3 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 y #s(literal -8/3 binary64)) x)
(fma.f64 #s(literal 1 binary64) (/.f64 y #s(literal -8/3 binary64)) (*.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal 1 binary64) (/.f64 y #s(literal -8/3 binary64)) (*.f64 x #s(literal 1 binary64)))
(fma.f64 #s(literal -1 binary64) (*.f64 y #s(literal 3/8 binary64)) x)
(fma.f64 #s(literal -1 binary64) (.f64 y #s(literal 3/8 binary64)) (.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal -1 binary64) (.f64 y #s(literal 3/8 binary64)) (.f64 x #s(literal 1 binary64)))
(fma.f64 #s(literal 3/8 binary64) (-.f64 #s(literal 0 binary64) y) x)
(fma.f64 #s(literal 3/8 binary64) (-.f64 #s(literal 0 binary64) y) (*.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal 3/8 binary64) (-.f64 #s(literal 0 binary64) y) (*.f64 x #s(literal 1 binary64)))
(fma.f64 (pow.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1/2 binary64)) x)
(fma.f64 (pow.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (pow.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1/2 binary64)) (*.f64 x #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal -8/3 binary64)) x) (/.f64 #s(literal -8/3 binary64) y))) (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (*.f64 y y)) #s(literal -512/27 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (.f64 y #s(literal 3/8 binary64))) (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64)))))
(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x)) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal -8/3 binary64)) x) (/.f64 #s(literal -8/3 binary64) y))) (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (*.f64 y y)) #s(literal -512/27 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x (.f64 y #s(literal 3/8 binary64))) (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x))) (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal -512/27 binary64))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal -8/3 binary64)) x) (/.f64 #s(literal -8/3 binary64) y))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal -512/27 binary64))) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 (*.f64 x x) (/.f64 x (/.f64 #s(literal -8/3 binary64) y)))))
(/.f64 (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64))) (+.f64 x (.f64 y #s(literal 3/8 binary64))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal -512/27 binary64)))) (neg.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal -8/3 binary64)) x) (/.f64 #s(literal -8/3 binary64) y)))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal -512/27 binary64)))) (neg.f64 (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 (*.f64 x x) (/.f64 x (/.f64 #s(literal -8/3 binary64) y))))))
(/.f64 (neg.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) #s(literal -9/64 binary64)))) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal -512/27 binary64)))) (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal -8/3 binary64)) x) (/.f64 #s(literal -8/3 binary64) y))))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64)))) (+.f64 x (*.f64 y #s(literal 3/8 binary64))))
(/.f64 (.f64 (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64))) #s(literal -1 binary64)) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x))
(/.f64 (.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal -512/27 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal -8/3 binary64)) x) (/.f64 #s(literal -8/3 binary64) y))))
(/.f64 (.f64 (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64))) #s(literal 1 binary64)) (+.f64 x (*.f64 y #s(literal 3/8 binary64))))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x (.f64 y #s(literal 3/8 binary64)))) (.f64 (+.f64 x (.f64 y #s(literal 3/8 binary64))) (.f64 y (.f64 y #s(literal 9/64 binary64))))) (.f64 (+.f64 x (.f64 y #s(literal 3/8 binary64))) (+.f64 x (.f64 y #s(literal 3/8 binary64)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal -512/27 binary64))))) (neg.f64 (neg.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal -8/3 binary64)) x) (/.f64 #s(literal -8/3 binary64) y))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) #s(literal -9/64 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)))
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(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (/.f64 y #s(literal -8/3 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 y #s(literal -8/3 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal -8/3 binary64) y)) #s(literal -2 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 y (*.f64 y #s(literal 9/64 binary64))))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 8/3 binary64) y)) (/.f64 (/.f64 y #s(literal -8/3 binary64)) (/.f64 #s(literal 8/3 binary64) y)))
(/.f64 (/.f64 y #s(literal -8/3 binary64)) (/.f64 #s(literal -8/3 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y #s(literal 9/64 binary64)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (/.f64 #s(literal -8/3 binary64) y) (/.f64 #s(literal 8/3 binary64) y))))
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (/.f64 #s(literal 8/3 binary64) y) (/.f64 #s(literal -8/3 binary64) y))))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -8/3 binary64) y) (/.f64 #s(literal 8/3 binary64) y)))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 8/3 binary64) y) (/.f64 #s(literal -8/3 binary64) y)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y #s(literal 9/64 binary64))))))
(/.f64 (*.f64 y #s(literal 3/8 binary64)) (/.f64 #s(literal 8/3 binary64) y))
(/.f64 (*.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 8/3 binary64) y))
(/.f64 (neg.f64 (*.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal -8/3 binary64) y))
(pow.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal -8/3 binary64) y) #s(literal -2 binary64))
(pow.f64 (*.f64 y #s(literal 3/8 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y #s(literal 9/64 binary64)))) #s(literal -1 binary64))
(.f64 y (.f64 y #s(literal 9/64 binary64)))
(.f64 y (.f64 #s(literal -3/8 binary64) (/.f64 y #s(literal -8/3 binary64))))
(.f64 #s(literal -3/8 binary64) (.f64 y (/.f64 y #s(literal -8/3 binary64))))
(*.f64 (/.f64 y #s(literal -8/3 binary64)) (/.f64 y #s(literal -8/3 binary64)))
(.f64 #s(literal 1 binary64) (.f64 y (*.f64 y #s(literal 9/64 binary64))))
(*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 8/3 binary64) y) #s(literal -2 binary64)))
(.f64 (.f64 y y) #s(literal 9/64 binary64))
(.f64 #s(literal 9/64 binary64) (.f64 y y))
(*.f64 #s(literal 9/64 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 2 binary64)))
(*.f64 #s(literal 9/64 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -2 binary64)))
(*.f64 #s(literal 9/64 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) #s(literal -2 binary64)))
(*.f64 #s(literal 9/64 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) y)) #s(literal -2 binary64)))
(.f64 (.f64 y #s(literal 9/64 binary64)) y)
(.f64 (.f64 y (*.f64 y #s(literal 9/64 binary64))) #s(literal 1 binary64))
(.f64 (.f64 y #s(literal 3/8 binary64)) (*.f64 y #s(literal 3/8 binary64)))
(.f64 (.f64 (/.f64 y #s(literal -8/3 binary64)) y) #s(literal -3/8 binary64))
(.f64 (.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal -3/8 binary64)) y)
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -2 binary64)) #s(literal 9/64 binary64))
(*.f64 y #s(literal 9/64 binary64))
(*.f64 #s(literal 9/64 binary64) y)
(exp.f64 (.f64 (log.f64 (+.f64 x (.f64 y #s(literal 3/8 binary64)))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)))
(/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y #s(literal 3/8 binary64))))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)))
(/.f64 #s(literal -1 binary64) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x))
(/.f64 #s(literal -1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x))))
(pow.f64 (+.f64 x (*.f64 y #s(literal 3/8 binary64))) #s(literal -1 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 x (*.f64 y #s(literal 3/8 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (+.f64 x (.f64 y #s(literal 3/8 binary64))) (+.f64 x (*.f64 y #s(literal 3/8 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 x (*.f64 y #s(literal 3/8 binary64))))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (.f64 y #s(literal 3/8 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (.f64 y #s(literal 3/8 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)))
(.f64 (pow.f64 (+.f64 x (.f64 y #s(literal 3/8 binary64))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 x (*.f64 y #s(literal 3/8 binary64))) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 27/512 binary64)))) (+.f64 (.f64 x x) (.f64 (/.f64 y #s(literal -8/3 binary64)) (+.f64 x (/.f64 y #s(literal -8/3 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 27/512 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (/.f64 y #s(literal -8/3 binary64)) (+.f64 x (/.f64 y #s(literal -8/3 binary64)))))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64)))) (+.f64 x (/.f64 y #s(literal -8/3 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal -8/3 binary64)))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64))) (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x (.f64 y #s(literal 3/8 binary64)))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal -9/64 binary64))) (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal -512/27 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal -8/3 binary64)) x) (/.f64 #s(literal -8/3 binary64) y)))))
(exp.f64 (log.f64 (/.f64 y #s(literal -8/3 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 y #s(literal 8/3 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 y #s(literal 3/8 binary64))) (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 y #s(literal 3/8 binary64))))
(neg.f64 (*.f64 y #s(literal 3/8 binary64)))
(/.f64 y #s(literal -8/3 binary64))
(/.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -8/3 binary64) y))
(/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (/.f64 y #s(literal -8/3 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 8/3 binary64) y))
(/.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 8/3 binary64))
(/.f64 (.f64 (.f64 y y) #s(literal -9/64 binary64)) (*.f64 y #s(literal 3/8 binary64)))
(/.f64 (neg.f64 (.f64 (.f64 y y) #s(literal -9/64 binary64))) (/.f64 y #s(literal -8/3 binary64)))
(/.f64 #s(literal 3/8 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) y)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) y)) #s(literal -8/3 binary64))
(/.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) #s(literal -3/8 binary64)) y)
(/.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) y) #s(literal -3/8 binary64))
(/.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) #s(literal 1 binary64)) (/.f64 y #s(literal -8/3 binary64)))
(/.f64 (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) #s(literal -3/8 binary64))) (-.f64 #s(literal 0 binary64) y))
(/.f64 (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) y)) #s(literal 3/8 binary64))
(/.f64 (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) #s(literal 1 binary64))) (*.f64 y #s(literal 3/8 binary64)))
(pow.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal -8/3 binary64) y) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y #s(literal 9/64 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 y (*.f64 y #s(literal 9/64 binary64)))) (/.f64 y #s(literal -8/3 binary64))) #s(literal -1 binary64))
(*.f64 y #s(literal -3/8 binary64))
(.f64 y (/.f64 (.f64 y #s(literal 9/64 binary64)) (/.f64 y #s(literal -8/3 binary64))))
(*.f64 #s(literal -3/8 binary64) y)
(.f64 #s(literal -3/8 binary64) (/.f64 (.f64 y y) y))
(*.f64 #s(literal -3/8 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 y #s(literal -8/3 binary64)))
(.f64 (.f64 y y) (/.f64 #s(literal 9/64 binary64) (/.f64 y #s(literal -8/3 binary64))))
(.f64 #s(literal 9/64 binary64) (/.f64 (.f64 y y) (/.f64 y #s(literal -8/3 binary64))))
(.f64 (.f64 y #s(literal 9/64 binary64)) (/.f64 y (/.f64 y #s(literal -8/3 binary64))))
(.f64 (.f64 y (*.f64 y #s(literal 9/64 binary64))) (/.f64 #s(literal -8/3 binary64) y))
(.f64 #s(literal -1 binary64) (.f64 y #s(literal 3/8 binary64)))
(*.f64 #s(literal 3/8 binary64) (-.f64 #s(literal 0 binary64) y))
(*.f64 #s(literal 3/8 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) y)) #s(literal -1 binary64)))
(.f64 (/.f64 y y) (/.f64 (.f64 y #s(literal 9/64 binary64)) #s(literal -3/8 binary64)))
(.f64 (/.f64 (.f64 y #s(literal 9/64 binary64)) #s(literal -3/8 binary64)) (/.f64 y y))
(.f64 (/.f64 y #s(literal -3/8 binary64)) (/.f64 (.f64 y #s(literal 9/64 binary64)) y))
(.f64 (/.f64 (.f64 y #s(literal 9/64 binary64)) y) (/.f64 y #s(literal -3/8 binary64)))
(.f64 (/.f64 y #s(literal 1 binary64)) (/.f64 (.f64 y #s(literal 9/64 binary64)) (/.f64 y #s(literal -8/3 binary64))))
(.f64 (/.f64 (.f64 y y) y) #s(literal -3/8 binary64))
(.f64 (/.f64 (.f64 y y) #s(literal -3/8 binary64)) (/.f64 #s(literal 9/64 binary64) y))
(.f64 (/.f64 #s(literal 9/64 binary64) y) (/.f64 (.f64 y y) #s(literal -3/8 binary64)))
(.f64 (/.f64 (.f64 y y) #s(literal 1 binary64)) (/.f64 #s(literal 9/64 binary64) (/.f64 y #s(literal -8/3 binary64))))
(.f64 (/.f64 (.f64 y #s(literal 9/64 binary64)) #s(literal 1 binary64)) (/.f64 y (/.f64 y #s(literal -8/3 binary64))))
(*.f64 (pow.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1/2 binary64)))
(.f64 (/.f64 (.f64 y (*.f64 y #s(literal 9/64 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal -8/3 binary64) y))
(.f64 (/.f64 (.f64 y (*.f64 y #s(literal 9/64 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 8/3 binary64) y))

simplify309.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

4292×	`-lowering-.f32`
4292×	`-lowering-.f64`
2982×	`/-lowering-/.f32`
2982×	`/-lowering-/.f64`
1862×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	341	2804
1	1113	2496
2	3189	2428
0	8916	2428

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 384

Calls

Call 1

Inputs
(* -3/8 y)
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(+ x (* -3/8 y))
x
(* x (+ 1 (* -3/8 (/ y x))))
(* x (+ 1 (* -3/8 (/ y x))))
(* x (+ 1 (* -3/8 (/ y x))))
x
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
x
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(* -3/8 y)
(* y (- (/ x y) 3/8))
(* y (- (/ x y) 3/8))
(* y (- (/ x y) 3/8))
(* -3/8 y)
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
(* -3/8 y)
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(+ x (* -3/8 y))
x
(* x (+ 1 (* -3/8 (/ y x))))
(* x (+ 1 (* -3/8 (/ y x))))
(* x (+ 1 (* -3/8 (/ y x))))
x
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
x
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(* -3/8 y)
(* y (- (/ x y) 3/8))
(* y (- (/ x y) 3/8))
(* y (- (/ x y) 3/8))
(* -3/8 y)
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(* -3/8 y)
(+ x (* -3/8 y))
(+ (* -3/8 y) (* x (+ 1 (* -8/3 (/ x y)))))
(+ (* -3/8 y) (* x (+ 1 (* x (- (* 64/9 (/ x (pow y 2))) (* 8/3 (/ 1 y)))))))
(* -9/64 (/ (pow y 2) x))
(/ (+ (* -9/64 (pow y 2)) (* 27/512 (/ (pow y 3) x))) x)
(/ (+ (* -9/64 (pow y 2)) (+ (* -81/4096 (/ (pow y 4) (pow x 2))) (* 27/512 (/ (pow y 3) x)))) x)
(/ (+ (* -9/64 (pow y 2)) (+ (* -81/4096 (/ (pow y 4) (pow x 2))) (+ (* 243/32768 (/ (pow y 5) (pow x 3))) (* 27/512 (/ (pow y 3) x))))) x)
(* -9/64 (/ (pow y 2) x))
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(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* -243/32768 (/ (pow y 5) x)) (* -81/4096 (pow y 4))) x)) (* -27/512 (pow y 3))) x)) (* 9/64 (pow y 2))) x))
(* -9/64 (/ (pow y 2) x))
(* (pow y 2) (- (* 27/512 (/ y (pow x 2))) (* 9/64 (/ 1 x))))
(* (pow y 2) (- (* y (+ (* -81/4096 (/ y (pow x 3))) (* 27/512 (/ 1 (pow x 2))))) (* 9/64 (/ 1 x))))
(* (pow y 2) (- (* y (+ (* y (- (* 243/32768 (/ y (pow x 4))) (* 81/4096 (/ 1 (pow x 3))))) (* 27/512 (/ 1 (pow x 2))))) (* 9/64 (/ 1 x))))
(* -3/8 y)
(* y (- (/ x y) 3/8))
(* y (- (* -8/3 (/ (pow x 2) (pow y 2))) (+ 3/8 (* -1 (/ x y)))))
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(* -3/8 y)
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(* -1 (* y (+ 3/8 (* -1 (/ (- (* -8/3 (/ (pow x 2) y)) (* -1 x)) y)))))
(* -1 (* y (+ 3/8 (* -1 (/ (- (* -1 (/ (- (* -64/9 (/ (pow x 3) y)) (* -8/3 (pow x 2))) y)) (* -1 x)) y)))))
(/ -8/3 y)
(- (* -64/9 (/ x (pow y 2))) (* 8/3 (/ 1 y)))
(- (* -64/9 (/ x (pow y 2))) (* 8/3 (/ 1 y)))
(- (* -64/9 (/ x (pow y 2))) (* 8/3 (/ 1 y)))
(* -64/9 (/ x (pow y 2)))
(* -1 (* x (+ (* 8/3 (/ 1 (* x y))) (* 64/9 (/ 1 (pow y 2))))))
(* -1 (* x (+ (* 8/3 (/ 1 (* x y))) (* 64/9 (/ 1 (pow y 2))))))
(* -1 (* x (+ (* 8/3 (/ 1 (* x y))) (* 64/9 (/ 1 (pow y 2))))))
(* -64/9 (/ x (pow y 2)))
(* -1 (* x (+ (* 8/3 (/ 1 (* x y))) (* 64/9 (/ 1 (pow y 2))))))
(* -1 (* x (+ (* 8/3 (/ 1 (* x y))) (* 64/9 (/ 1 (pow y 2))))))
(* -1 (* x (+ (* 8/3 (/ 1 (* x y))) (* 64/9 (/ 1 (pow y 2))))))
(* -64/9 (/ x (pow y 2)))
(/ (+ (* -64/9 x) (* -8/3 y)) (pow y 2))
(/ (+ (* -64/9 x) (* -8/3 y)) (pow y 2))
(/ (+ (* -64/9 x) (* -8/3 y)) (pow y 2))
(/ -8/3 y)
(/ (- (* -64/9 (/ x y)) 8/3) y)
(/ (- (* -64/9 (/ x y)) 8/3) y)
(/ (- (* -64/9 (/ x y)) 8/3) y)
(/ -8/3 y)
(* -1 (/ (+ 8/3 (* 64/9 (/ x y))) y))
(* -1 (/ (+ 8/3 (* 64/9 (/ x y))) y))
(* -1 (/ (+ 8/3 (* 64/9 (/ x y))) y))
-8/3
(- (* -64/9 (/ x y)) 8/3)
(- (* -64/9 (/ x y)) 8/3)
(- (* -64/9 (/ x y)) 8/3)
(* -64/9 (/ x y))
(* -1 (* x (+ (* 64/9 (/ 1 y)) (* 8/3 (/ 1 x)))))
(* -1 (* x (+ (* 64/9 (/ 1 y)) (* 8/3 (/ 1 x)))))
(* -1 (* x (+ (* 64/9 (/ 1 y)) (* 8/3 (/ 1 x)))))
(* -64/9 (/ x y))
(* -1 (* x (+ (* 8/3 (/ 1 x)) (* 64/9 (/ 1 y)))))
(* -1 (* x (+ (* 8/3 (/ 1 x)) (* 64/9 (/ 1 y)))))
(* -1 (* x (+ (* 8/3 (/ 1 x)) (* 64/9 (/ 1 y)))))
(* -64/9 (/ x y))
(/ (+ (* -64/9 x) (* -8/3 y)) y)
(/ (+ (* -64/9 x) (* -8/3 y)) y)
(/ (+ (* -64/9 x) (* -8/3 y)) y)
-8/3
(- (* -64/9 (/ x y)) 8/3)
(- (* -64/9 (/ x y)) 8/3)
(- (* -64/9 (/ x y)) 8/3)
-8/3
(- (* -64/9 (/ x y)) 8/3)
(- (* -64/9 (/ x y)) 8/3)
(- (* -64/9 (/ x y)) 8/3)
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -64/9 (/ x y))
(* -9/64 (/ (pow y 2) x))
(* (pow y 2) (- (* 27/512 (/ y (pow x 2))) (* 9/64 (/ 1 x))))
(* (pow y 2) (- (* y (+ (* -81/4096 (/ y (pow x 3))) (* 27/512 (/ 1 (pow x 2))))) (* 9/64 (/ 1 x))))
(* (pow y 2) (- (* y (+ (* y (- (* 243/32768 (/ y (pow x 4))) (* 81/4096 (/ 1 (pow x 3))))) (* 27/512 (/ 1 (pow x 2))))) (* 9/64 (/ 1 x))))
(* -3/8 y)
(* y (- (/ x y) 3/8))
(* y (- (* -8/3 (/ (pow x 2) (pow y 2))) (+ 3/8 (* -1 (/ x y)))))
(* y (- (* 64/9 (/ (pow x 3) (pow y 3))) (+ 3/8 (+ (* -1 (/ x y)) (* 8/3 (/ (pow x 2) (pow y 2)))))))
(* -3/8 y)
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -1 (* y (+ 3/8 (* -1 (/ (- (* -8/3 (/ (pow x 2) y)) (* -1 x)) y)))))
(* -1 (* y (+ 3/8 (* -1 (/ (- (* -1 (/ (- (* -64/9 (/ (pow x 3) y)) (* -8/3 (pow x 2))) y)) (* -1 x)) y)))))
(* -3/8 y)
(+ x (* -3/8 y))
(+ (* -3/8 y) (* x (+ 1 (* -8/3 (/ x y)))))
(+ (* -3/8 y) (* x (+ 1 (* x (- (* 64/9 (/ x (pow y 2))) (* 8/3 (/ 1 y)))))))
(* -9/64 (/ (pow y 2) x))
(/ (+ (* -9/64 (pow y 2)) (* 27/512 (/ (pow y 3) x))) x)
(/ (+ (* -9/64 (pow y 2)) (+ (* -81/4096 (/ (pow y 4) (pow x 2))) (* 27/512 (/ (pow y 3) x)))) x)
(/ (+ (* -9/64 (pow y 2)) (+ (* -81/4096 (/ (pow y 4) (pow x 2))) (+ (* 243/32768 (/ (pow y 5) (pow x 3))) (* 27/512 (/ (pow y 3) x))))) x)
(* -9/64 (/ (pow y 2) x))
(* -1 (/ (+ (* -27/512 (/ (pow y 3) x)) (* 9/64 (pow y 2))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -81/4096 (/ (pow y 4) x)) (* 27/512 (pow y 3))) x)) (* 9/64 (pow y 2))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -243/32768 (/ (pow y 5) x)) (* 81/4096 (pow y 4))) x)) (* 27/512 (pow y 3))) x)) (* 9/64 (pow y 2))) x))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* -1 x)
(- (* -3/8 y) x)
(- (* -3/8 y) x)
(- (* -3/8 y) x)
(* -3/8 y)
(* y (- (* -1 (/ x y)) 3/8))
(* y (- (* -1 (/ x y)) 3/8))
(* y (- (* -1 (/ x y)) 3/8))
(* -3/8 y)
(* -1 (* y (+ 3/8 (/ x y))))
(* -1 (* y (+ 3/8 (/ x y))))
(* -1 (* y (+ 3/8 (/ x y))))
(* -3/8 y)
(+ (* -1 x) (* -3/8 y))
(+ (* -1 x) (* -3/8 y))
(+ (* -1 x) (* -3/8 y))
(* -1 x)
(* x (- (* -3/8 (/ y x)) 1))
(* x (- (* -3/8 (/ y x)) 1))
(* x (- (* -3/8 (/ y x)) 1))
(* -1 x)
(* -1 (* x (+ 1 (* 3/8 (/ y x)))))
(* -1 (* x (+ 1 (* 3/8 (/ y x)))))
(* -1 (* x (+ 1 (* 3/8 (/ y x)))))
(* 8/3 (/ (pow x 2) y))
(/ (+ (* -3/8 (pow y 2)) (* 8/3 (pow x 2))) y)
(/ (+ (* -3/8 (pow y 2)) (* 8/3 (pow x 2))) y)
(/ (+ (* -3/8 (pow y 2)) (* 8/3 (pow x 2))) y)
(* -3/8 y)
(* y (- (* 8/3 (/ (pow x 2) (pow y 2))) 3/8))
(* y (- (* 8/3 (/ (pow x 2) (pow y 2))) 3/8))
(* y (- (* 8/3 (/ (pow x 2) (pow y 2))) 3/8))
(* -3/8 y)
(* -1 (* y (+ 3/8 (* -8/3 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 3/8 (* -8/3 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 3/8 (* -8/3 (/ (pow x 2) (pow y 2))))))
(* -3/8 y)
(+ (* -3/8 y) (* 8/3 (/ (pow x 2) y)))
(+ (* -3/8 y) (* 8/3 (/ (pow x 2) y)))
(+ (* -3/8 y) (* 8/3 (/ (pow x 2) y)))
(* 8/3 (/ (pow x 2) y))
(* (pow x 2) (+ (* -3/8 (/ y (pow x 2))) (* 8/3 (/ 1 y))))
(* (pow x 2) (+ (* -3/8 (/ y (pow x 2))) (* 8/3 (/ 1 y))))
(* (pow x 2) (+ (* -3/8 (/ y (pow x 2))) (* 8/3 (/ 1 y))))
(* 8/3 (/ (pow x 2) y))
(* (pow x 2) (+ (* -3/8 (/ y (pow x 2))) (* 8/3 (/ 1 y))))
(* (pow x 2) (+ (* -3/8 (/ y (pow x 2))) (* 8/3 (/ 1 y))))
(* (pow x 2) (+ (* -3/8 (/ y (pow x 2))) (* 8/3 (/ 1 y))))
(* -1 (pow x 2))
(- (* 9/64 (pow y 2)) (pow x 2))
(- (* 9/64 (pow y 2)) (pow x 2))
(- (* 9/64 (pow y 2)) (pow x 2))
(* 9/64 (pow y 2))
(* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))
(* 9/64 (pow y 2))
(* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 9/64 (* -1 (/ (pow x 2) (pow y 2)))))
(* 9/64 (pow y 2))
(+ (* -1 (pow x 2)) (* 9/64 (pow y 2)))
(+ (* -1 (pow x 2)) (* 9/64 (pow y 2)))
(+ (* -1 (pow x 2)) (* 9/64 (pow y 2)))
(* -1 (pow x 2))
(* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))
(* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))
(* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))
(* -1 (pow x 2))
(* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))
(* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))
(* (pow x 2) (- (* 9/64 (/ (pow y 2) (pow x 2))) 1))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 (pow y 2))
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(/ 8/3 y)
(+ (* -64/9 (/ x (pow y 2))) (* 8/3 (/ 1 y)))
(+ (* x (- (* 512/27 (/ x (pow y 3))) (* 64/9 (/ 1 (pow y 2))))) (* 8/3 (/ 1 y)))
(+ (* x (- (* x (+ (* -4096/81 (/ x (pow y 4))) (* 512/27 (/ 1 (pow y 3))))) (* 64/9 (/ 1 (pow y 2))))) (* 8/3 (/ 1 y)))
(/ 1 x)
(/ (+ 1 (* -3/8 (/ y x))) x)
(/ (- (+ 1 (* 9/64 (/ (pow y 2) (pow x 2)))) (* 3/8 (/ y x))) x)
(/ (- (+ 1 (* -27/512 (/ (pow y 3) (pow x 3)))) (+ (* -9/64 (/ (pow y 2) (pow x 2))) (* 3/8 (/ y x)))) x)
(/ 1 x)
(* -1 (/ (- (* 3/8 (/ y x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* 9/64 (/ (pow y 2) x)) (* 3/8 y)) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 27/512 (/ (pow y 3) x)) (* 9/64 (pow y 2))) x)) (* 3/8 y)) x)) 1) x))
(/ 1 x)
(+ (* -3/8 (/ y (pow x 2))) (/ 1 x))
(+ (* y (- (* 9/64 (/ y (pow x 3))) (* 3/8 (/ 1 (pow x 2))))) (/ 1 x))
(+ (* y (- (* y (+ (* -27/512 (/ y (pow x 4))) (* 9/64 (/ 1 (pow x 3))))) (* 3/8 (/ 1 (pow x 2))))) (/ 1 x))
(/ 8/3 y)
(/ (+ 8/3 (* -64/9 (/ x y))) y)
(/ (- (+ 8/3 (* 512/27 (/ (pow x 2) (pow y 2)))) (* 64/9 (/ x y))) y)
(/ (- (+ 8/3 (* -4096/81 (/ (pow x 3) (pow y 3)))) (+ (* -512/27 (/ (pow x 2) (pow y 2))) (* 64/9 (/ x y)))) y)
(/ 8/3 y)
(* -1 (/ (- (* 64/9 (/ x y)) 8/3) y))
(* -1 (/ (- (* -1 (/ (- (* 512/27 (/ (pow x 2) y)) (* 64/9 x)) y)) 8/3) y))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 4096/81 (/ (pow x 3) y)) (* 512/27 (pow x 2))) y)) (* 64/9 x)) y)) 8/3) y))
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)

Outputs
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
x
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 x (.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -3/8 binary64) y) #s(literal 1 binary64))))
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 x (.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -3/8 binary64) y) #s(literal 1 binary64))))
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 x (.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -3/8 binary64) y) #s(literal 1 binary64))))
x
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(+.f64 x (.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -3/8 binary64) y) #s(literal 1 binary64))))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(+.f64 x (.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -3/8 binary64) y) #s(literal 1 binary64))))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(+.f64 x (.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -3/8 binary64) y) #s(literal 1 binary64))))
x
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* y (- (/ x y) 3/8))
(*.f64 y (+.f64 #s(literal -3/8 binary64) (/.f64 x y)))
(* y (- (/ x y) 3/8))
(*.f64 y (+.f64 #s(literal -3/8 binary64) (/.f64 x y)))
(* y (- (/ x y) 3/8))
(*.f64 y (+.f64 #s(literal -3/8 binary64) (/.f64 x y)))
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(*.f64 y (+.f64 #s(literal -3/8 binary64) (/.f64 x y)))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(*.f64 y (+.f64 #s(literal -3/8 binary64) (/.f64 x y)))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(*.f64 y (+.f64 #s(literal -3/8 binary64) (/.f64 x y)))
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
x
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 x (.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -3/8 binary64) y) #s(literal 1 binary64))))
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 x (.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -3/8 binary64) y) #s(literal 1 binary64))))
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 x (.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -3/8 binary64) y) #s(literal 1 binary64))))
x
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
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(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(+.f64 x (.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -3/8 binary64) y) #s(literal 1 binary64))))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(+.f64 x (.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -3/8 binary64) y) #s(literal 1 binary64))))
x
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(+ x (* -3/8 y))
(+.f64 (*.f64 #s(literal -3/8 binary64) y) x)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* y (- (/ x y) 3/8))
(*.f64 y (+.f64 #s(literal -3/8 binary64) (/.f64 x y)))
(* y (- (/ x y) 3/8))
(*.f64 y (+.f64 #s(literal -3/8 binary64) (/.f64 x y)))
(* y (- (/ x y) 3/8))
(*.f64 y (+.f64 #s(literal -3/8 binary64) (/.f64 x y)))
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(*.f64 y (+.f64 #s(literal -3/8 binary64) (/.f64 x y)))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(*.f64 y (+.f64 #s(literal -3/8 binary64) (/.f64 x y)))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
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(/.f64 (+.f64 #s(literal 8/3 binary64) (/.f64 (+.f64 (.f64 x #s(literal -64/9 binary64)) (/.f64 (.f64 (*.f64 x x) #s(literal 512/27 binary64)) y)) y)) y)
(/ (- (+ 8/3 (* -4096/81 (/ (pow x 3) (pow y 3)))) (+ (* -512/27 (/ (pow x 2) (pow y 2))) (* 64/9 (/ x y)))) y)
(/.f64 (+.f64 #s(literal 8/3 binary64) (+.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -4096/81 binary64)) (.f64 y (.f64 y y))) (/.f64 (+.f64 (.f64 x #s(literal -64/9 binary64)) (/.f64 (.f64 (.f64 x x) #s(literal 512/27 binary64)) y)) y))) y)
(/ 8/3 y)
(/.f64 #s(literal 8/3 binary64) y)
(* -1 (/ (- (* 64/9 (/ x y)) 8/3) y))
(/.f64 (-.f64 #s(literal 8/3 binary64) (/.f64 (*.f64 x #s(literal 64/9 binary64)) y)) y)
(* -1 (/ (- (* -1 (/ (- (* 512/27 (/ (pow x 2) y)) (* 64/9 x)) y)) 8/3) y))
(/.f64 (+.f64 #s(literal 8/3 binary64) (/.f64 (+.f64 (.f64 x #s(literal -64/9 binary64)) (/.f64 (.f64 (*.f64 x x) #s(literal 512/27 binary64)) y)) y)) y)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 4096/81 (/ (pow x 3) y)) (* 512/27 (pow x 2))) y)) (* 64/9 x)) y)) 8/3) y))
(/.f64 (+.f64 #s(literal 8/3 binary64) (/.f64 (-.f64 (.f64 x #s(literal -64/9 binary64)) (/.f64 (+.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 4096/81 binary64)) y) (.f64 (.f64 x x) #s(literal -512/27 binary64))) y)) y)) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)

eval265.0ms (3.2%)

Compiler: Compiled 32651 to 2942 computations (91% saved)

prune188.0ms (2.3%)

Pruning

11 alts after pruning (6 fresh and 5 done)

	Pruned	Kept	Total
New	1531	6	1537
Fresh	1	0	1
Picked	3	2	5
Done	2	3	5
Total	1537	11	1548

Accuracy

100.0%

Counts

1548 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.0%	(/.f64 y #s(literal -8/3 binary64))
▶	52.0%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -3/8 binary64)))
✓	52.4%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -8/3 binary64) (*.f64 (/.f64 x y) #s(literal -64/9 binary64))) y))
✓	52.0%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -8/3 binary64) y))
▶	52.1%	(/.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) y))
▶	99.8%	(+.f64 (/.f64 y #s(literal -8/3 binary64)) x)
✓	99.9%	(+.f64 x (*.f64 y #s(literal -3/8 binary64)))
▶	52.0%	(.f64 (/.f64 (.f64 y #s(literal 9/64 binary64)) #s(literal -3/8 binary64)) (/.f64 y y))
	19.0%	(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 8/3 binary64) y) (.f64 #s(literal -3/8 binary64) (/.f64 y (.f64 x x)))))
✓	52.1%	(*.f64 #s(literal -3/8 binary64) y)
✓	48.8%	x

Compiler

Compiled 147 to 107 computations (27.2% saved)

simplify490.0ms (6%)

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 y #s(literal 9/64 binary64))
✓	cost-diff	128	(/.f64 y y)
✓	cost-diff	128	(/.f64 (*.f64 y #s(literal 9/64 binary64)) #s(literal -3/8 binary64))
✓	cost-diff	384	(.f64 (/.f64 (.f64 y #s(literal 9/64 binary64)) #s(literal -3/8 binary64)) (/.f64 y y))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) y)
✓	cost-diff	128	(/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -3/8 binary64))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -3/8 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) y)
✓	cost-diff	128	(/.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) y))
✓	cost-diff	0	(/.f64 y #s(literal -8/3 binary64))
✓	cost-diff	0	(/.f64 y #s(literal -8/3 binary64))
✓	cost-diff	0	(+.f64 (/.f64 y #s(literal -8/3 binary64)) x)

Rules

6942×	`-lowering-.f32`
6942×	`-lowering-.f64`
4694×	`associate-/r/`
2846×	`/-lowering-/.f32`
2846×	`/-lowering-/.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	49
1	35	48
2	59	48
3	122	47
4	543	47
5	2260	47
6	2533	47
7	2716	47
8	2912	47
9	3108	47
10	3299	47
11	3498	47
12	3705	47
13	3920	47
14	4143	47
15	4310	47
16	4419	47
17	4508	47
18	4508	47
0	8394	47

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (/ y -8/3) x)
(/ y -8/3)
y
-8/3
x
(/ y -8/3)
y
-8/3
(/ -3/8 (/ 1 y))
-3/8
(/ 1 y)
1
y
(/ 1 (/ (/ 1 y) -3/8))
1
(/ (/ 1 y) -3/8)
(/ 1 y)
y
-3/8
(* (/ (* y 9/64) -3/8) (/ y y))
(/ (* y 9/64) -3/8)
(* y 9/64)
y
9/64
-3/8
(/ y y)

Outputs
(+ (/ y -8/3) x)
(+.f64 x (/.f64 y #s(literal -8/3 binary64)))
(/ y -8/3)
(/.f64 y #s(literal -8/3 binary64))
y
-8/3
#s(literal -8/3 binary64)
x
(/ y -8/3)
(/.f64 y #s(literal -8/3 binary64))
y
-8/3
#s(literal -8/3 binary64)
(/ -3/8 (/ 1 y))
(/.f64 y #s(literal -8/3 binary64))
-3/8
#s(literal -3/8 binary64)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
1
#s(literal 1 binary64)
y
(/ 1 (/ (/ 1 y) -3/8))
(/.f64 y #s(literal -8/3 binary64))
1
#s(literal 1 binary64)
(/ (/ 1 y) -3/8)
(/.f64 #s(literal -8/3 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
y
-3/8
#s(literal -3/8 binary64)
(* (/ (* y 9/64) -3/8) (/ y y))
(/.f64 y #s(literal -8/3 binary64))
(/ (* y 9/64) -3/8)
(/.f64 y #s(literal -8/3 binary64))
(* y 9/64)
(/.f64 y #s(literal 64/9 binary64))
y
9/64
#s(literal 9/64 binary64)
-3/8
#s(literal -3/8 binary64)
(/ y y)
#s(literal 1 binary64)

localize213.0ms (2.6%)

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 y y)
✓	accuracy	100.0%	(.f64 (/.f64 (.f64 y #s(literal 9/64 binary64)) #s(literal -3/8 binary64)) (/.f64 y y))
✓	accuracy	100.0%	(*.f64 y #s(literal 9/64 binary64))
✓	accuracy	99.8%	(/.f64 (*.f64 y #s(literal 9/64 binary64)) #s(literal -3/8 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) y)
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -3/8 binary64)))
✓	accuracy	99.7%	(/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -3/8 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) y)
✓	accuracy	99.8%	(/.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) y))
✓	accuracy	99.8%	(/.f64 y #s(literal -8/3 binary64))
✓	accuracy	100.0%	(+.f64 (/.f64 y #s(literal -8/3 binary64)) x)
✓	accuracy	99.8%	(/.f64 y #s(literal -8/3 binary64))

Results

121.0ms	83×	5	exit
65.0ms	173×	0	valid

Compiler

Compiled 71 to 17 computations (76.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 89.0ms

ival-div: 35.0ms (39.2% of total)

...c/correct-round.rkt:119:19: 22.0ms (24.6% of total)

backward-pass: 14.0ms (15.7% of total)

ival-add: 10.0ms (11.2% of total)

ival-mult: 8.0ms (9% of total)

const: 1.0ms (1.1% of total)

series2.0ms (0%)

Counts

10 → 132

Calls

Call 1

Inputs
#<alt (+ (/ y -8/3) x)>
#<alt (/ y -8/3)>
#<alt (/ -3/8 (/ 1 y))>
#<alt (/ 1 y)>
#<alt (/ 1 (/ (/ 1 y) -3/8))>
#<alt (/ (/ 1 y) -3/8)>
#<alt (* (/ (* y 9/64) -3/8) (/ y y))>
#<alt (/ (* y 9/64) -3/8)>
#<alt (/ y y)>
#<alt (* y 9/64)>

Outputs
#<alt x>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (* -3/8 y)>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* y (- (/ x y) 3/8))>
#<alt (* -3/8 y)>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 3/8 (* -1 (/ x y)))))>
#<alt (* -3/8 y)>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt (+ x (* -3/8 y))>
#<alt x>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt (* x (+ 1 (* -3/8 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 3/8 (/ y x)) 1)))>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 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 (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (/ -8/3 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt (* -3/8 y)>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>
#<alt (* 9/64 y)>

Calls

33 calls:

Time	Variable		Point	Expression
0.0ms	y	@	-inf	(/ 1 y)
0.0ms	y	@	0	(/ 1 y)
0.0ms	y	@	0	(+ (/ y -8/3) x)
0.0ms	y	@	-inf	(* (/ (* y 9/64) -3/8) (/ y y))
0.0ms	y	@	inf	(* (/ (* y 9/64) -3/8) (/ y y))

rewrite445.0ms (5.4%)

Algorithm

1×	batch-egg-rewrite

Rules

4008×	`-lowering-.f32`
4008×	`-lowering-.f64`
2822×	`/-lowering-/.f32`
2822×	`/-lowering-/.f64`
1178×	`times-frac`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	30
1	90	28
2	603	28
3	7626	28
0	8002	28

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 1402

Calls

Call 1

Inputs
(+ (/ y -8/3) x)
(/ y -8/3)
(/ -3/8 (/ 1 y))
(/ 1 y)
(/ 1 (/ (/ 1 y) -3/8))
(/ (/ 1 y) -3/8)
(* (/ (* y 9/64) -3/8) (/ y y))
(/ (* y 9/64) -3/8)
(/ y y)
(* y 9/64)

Outputs
(+.f64 (/.f64 y #s(literal -8/3 binary64)) x)
(+.f64 x (/.f64 y #s(literal -8/3 binary64)))
(+.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)) (neg.f64 (*.f64 x (/.f64 x (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)))))
(-.f64 x (/.f64 y #s(literal 8/3 binary64)))
(-.f64 (/.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)) (*.f64 x (/.f64 x (-.f64 (/.f64 y #s(literal -8/3 binary64)) x))))
(-.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y #s(literal 8/3 binary64)))) (/.f64 (.f64 y (*.f64 y #s(literal 9/64 binary64))) (+.f64 x (/.f64 y #s(literal 8/3 binary64)))))
(fma.f64 y #s(literal -3/8 binary64) x)
(fma.f64 #s(literal -8/3 binary64) (*.f64 y #s(literal 9/64 binary64)) x)
(fma.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1 binary64) x)
(fma.f64 #s(literal -3/8 binary64) y x)
(fma.f64 #s(literal 1 binary64) (/.f64 y #s(literal -8/3 binary64)) x)
(fma.f64 #s(literal 9/64 binary64) (/.f64 y #s(literal -3/8 binary64)) x)
(fma.f64 (*.f64 y #s(literal 9/64 binary64)) #s(literal -8/3 binary64) x)
(fma.f64 #s(literal -1 binary64) (/.f64 y #s(literal 8/3 binary64)) x)
(fma.f64 #s(literal 3/8 binary64) (-.f64 #s(literal 0 binary64) y) x)
(fma.f64 (*.f64 y #s(literal -9/64 binary64)) #s(literal 8/3 binary64) x)
(fma.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 3/8 binary64) x)
(fma.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (/.f64 #s(literal -8/3 binary64) y) x)
(fma.f64 (*.f64 y (/.f64 y #s(literal -8/3 binary64))) (/.f64 #s(literal 1 binary64) y) x)
(fma.f64 (.f64 y (.f64 y #s(literal -9/64 binary64))) (/.f64 #s(literal 8/3 binary64) y) x)
(fma.f64 (pow.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 y (/.f64 y #s(literal 8/3 binary64))) (/.f64 #s(literal -1 binary64) y) x)
(neg.f64 (/.f64 (+.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal -512/27 binary64)) (.f64 x (.f64 x x))) (+.f64 (.f64 y (.f64 y #s(literal -9/64 binary64))) (neg.f64 (*.f64 x (+.f64 x (/.f64 y #s(literal 8/3 binary64))))))))
(neg.f64 (/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal -512/27 binary64)) (.f64 x (.f64 x x)))) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x (+.f64 x (/.f64 y #s(literal 8/3 binary64)))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x))) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 y #s(literal -8/3 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 y #s(literal -8/3 binary64)) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (/.f64 y #s(literal 8/3 binary64))) (+.f64 (.f64 x x) (.f64 y (*.f64 y #s(literal -9/64 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 y #s(literal -8/3 binary64)) x))))
(/.f64 (+.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal -512/27 binary64)) (.f64 x (.f64 x x))) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x (+.f64 x (/.f64 y #s(literal 8/3 binary64))))))
(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x)) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal -512/27 binary64)) (.f64 x (.f64 x x)))) (+.f64 (.f64 y (.f64 y #s(literal -9/64 binary64))) (neg.f64 (*.f64 x (+.f64 x (/.f64 y #s(literal 8/3 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x))) (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 y #s(literal -8/3 binary64)) x)))
(/.f64 (+.f64 (.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal -512/27 binary64)) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x (+.f64 x (/.f64 y #s(literal 8/3 binary64))))) (+.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal -512/27 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 729/262144 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x (+.f64 x (/.f64 y #s(literal 8/3 binary64))))) (-.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal -512/27 binary64)) (.f64 x (*.f64 x x)))))
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(.f64 (/.f64 (.f64 y (*.f64 y #s(literal 9/64 binary64))) #s(literal -8/3 binary64)) (/.f64 #s(literal -8/3 binary64) y))
(.f64 (/.f64 (.f64 y (*.f64 y #s(literal 9/64 binary64))) #s(literal 8/3 binary64)) (/.f64 #s(literal 8/3 binary64) y))
(.f64 (/.f64 #s(literal 9/64 binary64) y) (.f64 y y))
(.f64 (.f64 #s(literal -3/8 binary64) (*.f64 y #s(literal 9/64 binary64))) #s(literal -8/3 binary64))
(.f64 (.f64 #s(literal -3/8 binary64) (*.f64 y #s(literal -9/64 binary64))) #s(literal 8/3 binary64))
(.f64 (.f64 #s(literal -3/8 binary64) (pow.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1/2 binary64))) (pow.f64 (/.f64 y #s(literal -8/3 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal -3/8 binary64) (*.f64 y (/.f64 y #s(literal 8/3 binary64)))) (/.f64 #s(literal -1 binary64) y))
(.f64 (/.f64 (.f64 y (*.f64 y #s(literal 9/64 binary64))) (-.f64 #s(literal 0 binary64) y)) #s(literal -1 binary64))

simplify457.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

1744×	`fnmadd-define`
1606×	`fmsub-define`
1582×	`fnmsub-define`
1500×	`fma-lowering-fma.f32`
1500×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	390
1	73	372
2	193	372
3	505	372
4	1460	372
5	4059	372
6	6326	372
0	8037	372

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

Inputs
x
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(* -3/8 y)
(* y (- (/ x y) 3/8))
(* y (- (/ x y) 3/8))
(* y (- (/ x y) 3/8))
(* -3/8 y)
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(* -3/8 y)
(+ x (* -3/8 y))
(+ x (* -3/8 y))
(+ x (* -3/8 y))
x
(* x (+ 1 (* -3/8 (/ y x))))
(* x (+ 1 (* -3/8 (/ y x))))
(* x (+ 1 (* -3/8 (/ y x))))
x
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 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)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(/ -8/3 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
(* -3/8 y)
1
1
1
1
1
1
1
1
1
1
1
1
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)
(* 9/64 y)

Outputs
x
(+ x (* -3/8 y))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(+ x (* -3/8 y))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(+ x (* -3/8 y))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* y (- (/ x y) 3/8))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* y (- (/ x y) 3/8))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* y (- (/ x y) 3/8))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -1 (* y (+ 3/8 (* -1 (/ x y)))))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(+ x (* -3/8 y))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(+ x (* -3/8 y))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(+ x (* -3/8 y))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
x
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* x (+ 1 (* -3/8 (/ y x))))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
x
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -1 (* x (- (* 3/8 (/ y x)) 1)))
(+.f64 x (*.f64 #s(literal -3/8 binary64) y))
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 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)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(/ -8/3 y)
(/.f64 #s(literal -8/3 binary64) y)
(/ -8/3 y)
(/.f64 #s(literal -8/3 binary64) y)
(/ -8/3 y)
(/.f64 #s(literal -8/3 binary64) y)
(/ -8/3 y)
(/.f64 #s(literal -8/3 binary64) y)
(/ -8/3 y)
(/.f64 #s(literal -8/3 binary64) y)
(/ -8/3 y)
(/.f64 #s(literal -8/3 binary64) y)
(/ -8/3 y)
(/.f64 #s(literal -8/3 binary64) y)
(/ -8/3 y)
(/.f64 #s(literal -8/3 binary64) y)
(/ -8/3 y)
(/.f64 #s(literal -8/3 binary64) y)
(/ -8/3 y)
(/.f64 #s(literal -8/3 binary64) y)
(/ -8/3 y)
(/.f64 #s(literal -8/3 binary64) y)
(/ -8/3 y)
(/.f64 #s(literal -8/3 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
(* -3/8 y)
(*.f64 #s(literal -3/8 binary64) y)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
(* 9/64 y)
(*.f64 y #s(literal 9/64 binary64))
(* 9/64 y)
(*.f64 y #s(literal 9/64 binary64))
(* 9/64 y)
(*.f64 y #s(literal 9/64 binary64))
(* 9/64 y)
(*.f64 y #s(literal 9/64 binary64))
(* 9/64 y)
(*.f64 y #s(literal 9/64 binary64))
(* 9/64 y)
(*.f64 y #s(literal 9/64 binary64))
(* 9/64 y)
(*.f64 y #s(literal 9/64 binary64))
(* 9/64 y)
(*.f64 y #s(literal 9/64 binary64))
(* 9/64 y)
(*.f64 y #s(literal 9/64 binary64))
(* 9/64 y)
(*.f64 y #s(literal 9/64 binary64))
(* 9/64 y)
(*.f64 y #s(literal 9/64 binary64))
(* 9/64 y)
(*.f64 y #s(literal 9/64 binary64))

eval641.0ms (7.8%)

Compiler: Compiled 21086 to 1736 computations (91.8% saved)

prune227.0ms (2.8%)

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	1817	2	1819
Fresh	1	0	1
Picked	2	3	5
Done	2	3	5
Total	1822	8	1830

Accuracy

100.0%

Counts

1830 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.0%	(/.f64 y #s(literal -8/3 binary64))
✓	52.1%	(/.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) y))
	52.1%	(/.f64 #s(literal -8/3 binary64) (/.f64 #s(literal 64/9 binary64) y))
✓	99.8%	(+.f64 (/.f64 y #s(literal -8/3 binary64)) x)
	99.8%	(+.f64 (/.f64 #s(literal 3/8 binary64) (/.f64 #s(literal -1 binary64) y)) x)
✓	99.9%	(+.f64 x (*.f64 y #s(literal -3/8 binary64)))
✓	52.1%	(*.f64 #s(literal -3/8 binary64) y)
✓	48.8%	x

Compiler

Compiled 277 to 117 computations (57.8% saved)

regimes36.0ms (0.4%)

Counts

22 → 1

Calls

Call 1

Inputs
x
(*.f64 #s(literal -3/8 binary64) y)
(/.f64 y #s(literal -8/3 binary64))
(+.f64 x (*.f64 y #s(literal -3/8 binary64)))
(+.f64 (/.f64 y #s(literal -8/3 binary64)) x)
(/.f64 #s(literal -8/3 binary64) (/.f64 #s(literal 64/9 binary64) y))
(/.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -8/3 binary64) y))
(+.f64 (/.f64 #s(literal 3/8 binary64) (/.f64 #s(literal -1 binary64) y)) x)
(-.f64 x (*.f64 (/.f64 #s(literal 3 binary64) #s(literal 8 binary64)) y))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -3/8 binary64)))
(.f64 (/.f64 (.f64 y #s(literal 9/64 binary64)) #s(literal -3/8 binary64)) (/.f64 y y))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y #s(literal -3/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -8/3 binary64) (*.f64 (/.f64 x y) #s(literal -64/9 binary64))) y))
(/.f64 (.f64 (.f64 y y) #s(literal 9/64 binary64)) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x))
(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x)) (.f64 #s(literal -3/8 binary64) y))
(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 8/3 binary64) y) (.f64 #s(literal -3/8 binary64) (/.f64 y (.f64 x x)))))
(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x)) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))
(.f64 (+.f64 x (.f64 y #s(literal -3/8 binary64))) (.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y #s(literal -3/8 binary64))))))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 81/4096 binary64))) (.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 9/64 binary64))))))
(/.f64 (/.f64 (-.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) #s(literal 81/4096 binary64))) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x)))
(fma.f64 y #s(literal -3/8 binary64) x)

Outputs
(fma.f64 y #s(literal -3/8 binary64) x)

Calls

4 calls:

14.0ms	(*.f64 (/.f64 #s(literal 3 binary64) #s(literal 8 binary64)) y)
7.0ms	y
7.0ms	(-.f64 x (*.f64 (/.f64 #s(literal 3 binary64) #s(literal 8 binary64)) y))
6.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(-.f64 x (*.f64 (/.f64 #s(literal 3 binary64) #s(literal 8 binary64)) y))`
100.0%	1	`(*.f64 (/.f64 #s(literal 3 binary64) #s(literal 8 binary64)) y)`

Compiler

Compiled 22 to 17 computations (22.7% saved)

regimes29.0ms (0.4%)

Counts

21 → 1

Calls

Call 1

Inputs
x
(*.f64 #s(literal -3/8 binary64) y)
(/.f64 y #s(literal -8/3 binary64))
(+.f64 x (*.f64 y #s(literal -3/8 binary64)))
(+.f64 (/.f64 y #s(literal -8/3 binary64)) x)
(/.f64 #s(literal -8/3 binary64) (/.f64 #s(literal 64/9 binary64) y))
(/.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -8/3 binary64) y))
(+.f64 (/.f64 #s(literal 3/8 binary64) (/.f64 #s(literal -1 binary64) y)) x)
(-.f64 x (*.f64 (/.f64 #s(literal 3 binary64) #s(literal 8 binary64)) y))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -3/8 binary64)))
(.f64 (/.f64 (.f64 y #s(literal 9/64 binary64)) #s(literal -3/8 binary64)) (/.f64 y y))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y #s(literal -3/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -8/3 binary64) (*.f64 (/.f64 x y) #s(literal -64/9 binary64))) y))
(/.f64 (.f64 (.f64 y y) #s(literal 9/64 binary64)) (-.f64 (*.f64 y #s(literal -3/8 binary64)) x))
(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x)) (.f64 #s(literal -3/8 binary64) y))
(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 8/3 binary64) y) (.f64 #s(literal -3/8 binary64) (/.f64 y (.f64 x x)))))
(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (.f64 x x)) (-.f64 (.f64 y #s(literal -3/8 binary64)) x))
(.f64 (+.f64 x (.f64 y #s(literal -3/8 binary64))) (.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y #s(literal -3/8 binary64))))))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 81/4096 binary64))) (.f64 (-.f64 x (.f64 y #s(literal -3/8 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 9/64 binary64))))))
(/.f64 (/.f64 (-.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) #s(literal 81/4096 binary64))) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 y #s(literal -3/8 binary64)) x)) (+.f64 (.f64 y (.f64 y #s(literal 9/64 binary64))) (*.f64 x x)))

Outputs
(+.f64 x (*.f64 y #s(literal -3/8 binary64)))

Calls

4 calls:

8.0ms	(*.f64 (/.f64 #s(literal 3 binary64) #s(literal 8 binary64)) y)
7.0ms	y
6.0ms	(-.f64 x (*.f64 (/.f64 #s(literal 3 binary64) #s(literal 8 binary64)) y))
6.0ms	x

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(-.f64 x (*.f64 (/.f64 #s(literal 3 binary64) #s(literal 8 binary64)) y))`
99.9%	1	`(*.f64 (/.f64 #s(literal 3 binary64) #s(literal 8 binary64)) y)`

Compiler

Compiled 22 to 17 computations (22.7% saved)

regimes4.0ms (0%)

Counts

3 → 3

Calls

Call 1

Inputs
x
(*.f64 #s(literal -3/8 binary64) y)
(/.f64 y #s(literal -8/3 binary64))

Outputs
x
(*.f64 #s(literal -3/8 binary64) y)
x

Calls

2 calls:

2.0ms	x
2.0ms	y

Results

Accuracy	Segments	Branch
79.6%	3	`x`
77.8%	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
x

Outputs
x

Calls

2 calls:

2.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
48.8%	1	`y`
48.8%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch24.0ms (0.3%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	4.9896076294587566e-139	6.024252992037034e-133
8.0ms	-1.2062996711568837e+68	-1.5173300691389913e+67

Results

10.0ms	212×	0	valid
2.0ms	13×	2	valid
1.0ms	14×	1	valid
0.0ms	1×	3	valid

Compiler

Compiled 164 to 131 computations (20.1% saved)

Precisions

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

ival-div: 2.0ms (31.5% of total)

ival-mult: 2.0ms (31.5% of total)

ival-sub: 1.0ms (15.7% of total)

const: 0.0ms (0% of total)

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

simplify30.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`if-if-or-not_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	19	23

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 y #s(literal -3/8 binary64) x)
(+.f64 x (*.f64 y #s(literal -3/8 binary64)))
(if (<=.f64 x #s(literal -15499999999999999807248908482079906803750326892224135638178324283392 binary64)) x (if (<=.f64 x #s(literal 7672009237256583/12786682062094304179739022253232809188346257992355721833919106906625522642205759980012773798148063113870651109873281527379754908382364816614564560896 binary64)) (*.f64 #s(literal -3/8 binary64) y) x))
x

Outputs
(fma.f64 y #s(literal -3/8 binary64) x)
(+.f64 x (*.f64 y #s(literal -3/8 binary64)))
(if (<=.f64 x #s(literal -15499999999999999807248908482079906803750326892224135638178324283392 binary64)) x (if (<=.f64 x #s(literal 7672009237256583/12786682062094304179739022253232809188346257992355721833919106906625522642205759980012773798148063113870651109873281527379754908382364816614564560896 binary64)) (*.f64 #s(literal -3/8 binary64) y) x))
(if (<=.f64 x #s(literal -15499999999999999807248908482079906803750326892224135638178324283392 binary64)) x (if (<=.f64 x #s(literal 7672009237256583/12786682062094304179739022253232809188346257992355721833919106906625522642205759980012773798148063113870651109873281527379754908382364816614564560896 binary64)) (*.f64 y #s(literal -3/8 binary64)) x))
x

soundness770.0ms (9.4%)

Rules

3044×	`-lowering-.f32`
3044×	`-lowering-.f64`
2620×	`/-lowering-/.f32`
2620×	`/-lowering-/.f64`
1744×	`fnmadd-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	5
1	15	5
2	25	4
3	41	4
4	59	4
5	100	4
6	181	4
7	285	4
8	364	4
9	561	4
10	681	4
11	695	4
0	695	4
0	5	8
1	20	7
2	177	7
3	1925	7
0	8564	7
0	23	138
1	66	120
2	186	120
3	499	120
4	1449	120
5	4063	120
6	6264	120
0	8007	120

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	saturated

Compiler

Compiled 77 to 49 computations (36.4% saved)

preprocess28.0ms (0.3%)

Compiler: Compiled 68 to 38 computations (44.1% saved)

analyze0.0ms (0%)

sample776.0ms (9.5%)

preprocess49.0ms (0.6%)

explain163.0ms (2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize20.0ms (0.2%)

series2.0ms (0%)

rewrite349.0ms (4.3%)

simplify238.0ms (2.9%)

eval25.0ms (0.3%)

prune23.0ms (0.3%)

simplify190.0ms (2.3%)

localize122.0ms (1.5%)

series11.0ms (0.1%)

rewrite436.0ms (5.3%)

simplify244.0ms (3%)

eval251.0ms (3.1%)

prune118.0ms (1.4%)

simplify202.0ms (2.5%)

localize391.0ms (4.8%)

series34.0ms (0.4%)

rewrite394.0ms (4.8%)

simplify309.0ms (3.8%)

eval265.0ms (3.2%)

prune188.0ms (2.3%)

simplify490.0ms (6%)

localize213.0ms (2.6%)

series2.0ms (0%)

rewrite445.0ms (5.4%)

simplify457.0ms (5.6%)

eval641.0ms (7.8%)

prune227.0ms (2.8%)

regimes36.0ms (0.4%)

regimes29.0ms (0.4%)

regimes4.0ms (0%)

regimes3.0ms (0%)

bsearch24.0ms (0.3%)

simplify30.0ms (0.4%)

soundness770.0ms (9.4%)

preprocess28.0ms (0.3%)

end0.0ms (0%)

Profiling