Metrics for Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, 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 14 to 11 computations (21.4% saved)

Precisions

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

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

ival-add: 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)

sample872.0ms (8.1%)

Results

534.0ms

8256×

valid

Precisions

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

ival-mult: 155.0ms (49% of total)

ival-sub: 95.0ms (30% of total)

ival-add: 45.0ms (14.2% of total)

const: 19.0ms (6% of total)

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

Bogosity

preprocess216.0ms (2%)

Algorithm

2×	egg-herbie

Rules

1376×	`accelerator-lowering-fma.f32`
1376×	`accelerator-lowering-fma.f64`
862×	`sub-neg`
530×	`unsub-neg`
492×	`associate-+l-`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	72
1	82	70
2	209	66
3	666	56
4	1681	54
5	3183	54
6	3711	54
7	3848	54
8	3874	54
9	3878	54
10	3923	54
11	3983	54
12	4007	54
13	4007	54
14	4007	54
0	10	11
1	25	11
2	53	11
3	105	9
4	207	9
5	432	9
6	831	9
7	1224	9
8	1464	9
9	1485	9
0	1485	8

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(+ (- (* x (- y 1)) (* y 1/2)) 918938533204673/1000000000000000)

Outputs
(+ (- (* x (- y 1)) (* y 1/2)) 918938533204673/1000000000000000)
(+.f64 (*.f64 y (+.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))

Call 2

Inputs
(+ (- (* x (- y 1)) (* y 1/2)) 918938533204673/1000000000000000)
(+ (- (* (neg x) (- y 1)) (* y 1/2)) 918938533204673/1000000000000000)
(+ (- (* x (- (neg y) 1)) (* (neg y) 1/2)) 918938533204673/1000000000000000)
(neg (+ (- (* (neg x) (- y 1)) (* y 1/2)) 918938533204673/1000000000000000))
(neg (+ (- (* x (- (neg y) 1)) (* (neg y) 1/2)) 918938533204673/1000000000000000))
(+ (- (* y (- x 1)) (* x 1/2)) 918938533204673/1000000000000000)

Outputs
(+ (- (* x (- y 1)) (* y 1/2)) 918938533204673/1000000000000000)
(- 918938533204673/1000000000000000 (+ x (* y (- 1/2 x))))
(+ (- (* (neg x) (- y 1)) (* y 1/2)) 918938533204673/1000000000000000)
(+ x (+ 918938533204673/1000000000000000 (* y (- -1/2 x))))
(+ (- (* x (- (neg y) 1)) (* (neg y) 1/2)) 918938533204673/1000000000000000)
(+ (* y (- 1/2 x)) (- 918938533204673/1000000000000000 x))
(neg (+ (- (* (neg x) (- y 1)) (* y 1/2)) 918938533204673/1000000000000000))
(+ (* y (+ x 1/2)) (- -918938533204673/1000000000000000 x))
(neg (+ (- (* x (- (neg y) 1)) (* (neg y) 1/2)) 918938533204673/1000000000000000))
(+ x (- -918938533204673/1000000000000000 (* y (- 1/2 x))))
(+ (- (* y (- x 1)) (* x 1/2)) 918938533204673/1000000000000000)
(+ 918938533204673/1000000000000000 (- (* x (+ y -1/2)) y))

explain119.0ms (1.1%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`#s(literal 1/2 binary64)`
-	-	`(*.f64 y #s(literal 1/2 binary64))`
-	-	`y`
-	-	`(*.f64 x (-.f64 y #s(literal 1 binary64)))`
-	-	`#s(literal 918938533204673/1000000000000000 binary64)`
-	-	`(-.f64 (.f64 x (-.f64 y #s(literal 1 binary64))) (.f64 y #s(literal 1/2 binary64)))`
-	-	`(+.f64 (-.f64 (.f64 x (-.f64 y #s(literal 1 binary64))) (.f64 y #s(literal 1/2 binary64))) #s(literal 918938533204673/1000000000000000 binary64))`
-	-	`#s(literal 1 binary64)`
-	-	`(-.f64 y #s(literal 1 binary64))`

Results

72.0ms

512×

valid

Compiler

Compiled 91 to 64 computations (29.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-mult: 22.0ms (51.4% of total)

ival-sub: 15.0ms (35% of total)

const: 3.0ms (7% of total)

ival-add: 2.0ms (4.7% of total)

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

eval0.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (*.f64 y (+.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))

Compiler

Compiled 11 to 8 computations (27.3% saved)

localize130.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
✓	cost-diff	0	(+.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
✓	cost-diff	0	(+.f64 (*.f64 y (+.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
✓	accuracy	100.0%	(+.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
✓	accuracy	100.0%	(+.f64 (*.f64 y (+.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
✓	accuracy	100.0%	(*.f64 y (+.f64 x #s(literal -1/2 binary64)))

Rules

1376×	`accelerator-lowering-fma.f32`
1376×	`accelerator-lowering-fma.f64`
352×	`+-lowering-+.f64`
352×	`--lowering--.f32`
352×	`+-lowering-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	21	24
2	47	24
3	100	24
4	232	24
5	470	24
6	982	24
7	1345	24
8	1531	24
9	1565	24
0	1565	23

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* y (+ x -1/2)) (- 918938533204673/1000000000000000 x))
(* y (+ x -1/2))
y
(+ x -1/2)
x
-1/2
(- 918938533204673/1000000000000000 x)
918938533204673/1000000000000000

Outputs
(+ (* y (+ x -1/2)) (- 918938533204673/1000000000000000 x))
(+.f64 (*.f64 y (+.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* y (+ x -1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
y
(+ x -1/2)
(+.f64 x #s(literal -1/2 binary64))
x
-1/2
#s(literal -1/2 binary64)
(- 918938533204673/1000000000000000 x)
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
918938533204673/1000000000000000
#s(literal 918938533204673/1000000000000000 binary64)

Results

25.0ms

256×

valid

Compiler

Compiled 27 to 18 computations (33.3% saved)

Precisions

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

ival-add: 6.0ms (45.4% of total)

ival-mult: 4.0ms (30.3% of total)

ival-sub: 2.0ms (15.1% of total)

const: 1.0ms (7.6% of total)

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

series7.0ms (0.1%)

Counts

4 → 72

Calls

Call 1

Inputs
#<alt (* y (+ x -1/2))>
#<alt (+ (* y (+ x -1/2)) (- 918938533204673/1000000000000000 x))>
#<alt (- 918938533204673/1000000000000000 x)>
#<alt (+ x -1/2)>

Outputs
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 y) (* x y))>
#<alt (+ (* -1/2 y) (* x y))>
#<alt (+ (* -1/2 y) (* x y))>
#<alt (* x y)>
#<alt (* x (+ y (* -1/2 (/ y x))))>
#<alt (* x (+ y (* -1/2 (/ y x))))>
#<alt (* x (+ y (* -1/2 (/ y x))))>
#<alt (* x y)>
#<alt (* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))>
#<alt (- 918938533204673/1000000000000000 x)>
#<alt (- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)>
#<alt (- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)>
#<alt (- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)>
#<alt (* y (- x 1/2))>
#<alt (* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))>
#<alt (* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))>
#<alt (* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))>
#<alt (* y (- x 1/2))>
#<alt (* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))>
#<alt (* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))>
#<alt (* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))>
#<alt (+ 918938533204673/1000000000000000 (* -1/2 y))>
#<alt (+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))>
#<alt (+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))>
#<alt (+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))>
#<alt (* x (- y 1))>
#<alt (* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))>
#<alt (* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))>
#<alt (* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))>
#<alt (* -1 (* x (+ 1 (* -1 y))))>
#<alt (* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))>
#<alt 918938533204673/1000000000000000>
#<alt (+ 918938533204673/1000000000000000 (* -1 x))>
#<alt (+ 918938533204673/1000000000000000 (* -1 x))>
#<alt (+ 918938533204673/1000000000000000 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))>
#<alt (* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))>
#<alt (* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt -1/2>
#<alt (- x 1/2)>
#<alt (- x 1/2)>
#<alt (- x 1/2)>
#<alt x>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>

Calls

18 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* y (+ x -1/2))
0.0ms	y	@	0	(* y (+ x -1/2))
0.0ms	y	@	inf	(+ (* y (+ x -1/2)) (- 918938533204673/1000000000000000 x))
0.0ms	y	@	-inf	(* y (+ x -1/2))
0.0ms	y	@	inf	(* y (+ x -1/2))

rewrite615.0ms (5.7%)

Algorithm

1×	batch-egg-rewrite

Rules

6000×	`accelerator-lowering-fma.f32`
6000×	`accelerator-lowering-fma.f64`
5446×	`-lowering-.f32`
5446×	`-lowering-.f64`
4364×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	60	20
2	519	20
0	8507	19

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 372

Calls

Call 1

Inputs
(* y (+ x -1/2))
(+ (* y (+ x -1/2)) (- 918938533204673/1000000000000000 x))
(- 918938533204673/1000000000000000 x)
(+ x -1/2)

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

simplify422.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

9230×	`accelerator-lowering-fma.f32`
9230×	`accelerator-lowering-fma.f64`
1960×	`-lowering-.f32`
1960×	`-lowering-.f64`
1422×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	366
1	213	366
2	612	366
3	1865	366
4	5334	366
0	8217	347

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* -1/2 y)
(+ (* -1/2 y) (* x y))
(+ (* -1/2 y) (* x y))
(+ (* -1/2 y) (* x y))
(* x y)
(* x (+ y (* -1/2 (/ y x))))
(* x (+ y (* -1/2 (/ y x))))
(* x (+ y (* -1/2 (/ y x))))
(* x y)
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
(- 918938533204673/1000000000000000 x)
(- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)
(- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)
(- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)
(* y (- x 1/2))
(* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))
(* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))
(* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))
(* y (- x 1/2))
(* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))
(* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))
(* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))
(+ 918938533204673/1000000000000000 (* -1/2 y))
(+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))
(+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))
(+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))
(* x (- y 1))
(* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))
(* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))
(* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))
(* -1 (* x (+ 1 (* -1 y))))
(* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))
(* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))
(* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))
918938533204673/1000000000000000
(+ 918938533204673/1000000000000000 (* -1 x))
(+ 918938533204673/1000000000000000 (* -1 x))
(+ 918938533204673/1000000000000000 (* -1 x))
(* -1 x)
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(* -1 x)
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
-1/2
(- x 1/2)
(- x 1/2)
(- x 1/2)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (- 1 (* 1/2 (/ 1 x))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))

Outputs
(* y (- x 1/2))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(+ (* -1/2 y) (* x y))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(+ (* -1/2 y) (* x y))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(+ (* -1/2 y) (* x y))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* x y)
(*.f64 y x)
(* x (+ y (* -1/2 (/ y x))))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* x (+ y (* -1/2 (/ y x))))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* x (+ y (* -1/2 (/ y x))))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* x y)
(*.f64 y x)
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(- 918938533204673/1000000000000000 x)
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* y (- x 1/2))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* y (- x 1/2))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(+ 918938533204673/1000000000000000 (* -1/2 y))
(+.f64 (*.f64 y #s(literal -1/2 binary64)) #s(literal 918938533204673/1000000000000000 binary64))
(+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* x (- y 1))
(*.f64 x (+.f64 y #s(literal -1 binary64)))
(* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* -1 (* x (+ 1 (* -1 y))))
(*.f64 x (+.f64 y #s(literal -1 binary64)))
(* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))
(+.f64 (*.f64 y (-.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
918938533204673/1000000000000000
#s(literal 918938533204673/1000000000000000 binary64)
(+ 918938533204673/1000000000000000 (* -1 x))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(+ 918938533204673/1000000000000000 (* -1 x))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(+ 918938533204673/1000000000000000 (* -1 x))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
-1/2
#s(literal -1/2 binary64)
(- x 1/2)
(-.f64 x #s(literal 1/2 binary64))
(- x 1/2)
(-.f64 x #s(literal 1/2 binary64))
(- x 1/2)
(-.f64 x #s(literal 1/2 binary64))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(-.f64 x #s(literal 1/2 binary64))
(* x (- 1 (* 1/2 (/ 1 x))))
(-.f64 x #s(literal 1/2 binary64))
(* x (- 1 (* 1/2 (/ 1 x))))
(-.f64 x #s(literal 1/2 binary64))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/2 binary64))

eval155.0ms (1.4%)

Compiler: Compiled 13952 to 8416 computations (39.7% saved)

prune58.0ms (0.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	438	6	444
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	439	6	445

Accuracy

100.0%

Counts

445 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	66.0%	(fma.f64 (.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (.f64 y (+.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 y (+.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
▶	54.3%	(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
▶	66.6%	(+.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (/.f64 (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))))
▶	51.4%	(+.f64 (*.f64 y #s(literal -1/2 binary64)) #s(literal 918938533204673/1000000000000000 binary64))
▶	47.3%	(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
▶	49.7%	(*.f64 x (+.f64 y #s(literal -1 binary64)))

Compiler

Compiled 146 to 106 computations (27.4% saved)

localize449.0ms (4.2%)

Algorithm

1×	egg-herbie

Localize:

Found 22 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 y #s(literal -1/2 binary64))
✓	cost-diff	0	(+.f64 (*.f64 y #s(literal -1/2 binary64)) #s(literal 918938533204673/1000000000000000 binary64))
✓	cost-diff	0	(-.f64 x #s(literal 1/2 binary64))
✓	cost-diff	0	(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(+.f64 y #s(literal -1 binary64))
✓	cost-diff	0	(*.f64 x (+.f64 y #s(literal -1 binary64)))
✓	cost-diff	0	(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))
✓	cost-diff	0	(+.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
✓	cost-diff	0	(+.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (/.f64 (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))))
✓	accuracy	100.0%	(*.f64 y #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 (*.f64 y #s(literal -1/2 binary64)) #s(literal 918938533204673/1000000000000000 binary64))
✓	accuracy	100.0%	(-.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(+.f64 y #s(literal -1 binary64))
✓	accuracy	100.0%	(*.f64 x (+.f64 y #s(literal -1 binary64)))
✓	accuracy	100.0%	(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
✓	accuracy	100.0%	(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	65.8%	(/.f64 (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))

Rules

2912×	`accelerator-lowering-fma.f32`
2912×	`accelerator-lowering-fma.f64`
824×	`-lowering-.f32`
824×	`-lowering-.f64`
592×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	101
1	61	101
2	105	101
3	183	101
4	349	101
5	673	101
6	1321	101
7	1987	101
8	2536	101
9	2795	101
10	2950	101
11	3089	101
12	3104	101
13	3122	101
14	3124	101
15	3124	101
0	3124	96

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* y (+ x -1/2)) (/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x))) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000)))))
(* y (+ x -1/2))
y
(+ x -1/2)
x
-1/2
(/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x))) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000))))
(- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x)))
775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000
(* x (* x x))
(* x x)
(+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000)))
844448027808355901771309036929/1000000000000000000000000000000
(* x (+ x 918938533204673/1000000000000000))
(+ x 918938533204673/1000000000000000)
918938533204673/1000000000000000
(- 918938533204673/1000000000000000 x)
(* x (+ y -1))
(+ y -1)
-1
(* y (- x 1/2))
(- x 1/2)
1/2
(+ (* y -1/2) 918938533204673/1000000000000000)
(* y -1/2)

Outputs
(+ (* y (+ x -1/2)) (/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x))) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000)))))
(+.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (/.f64 (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))))
(* y (+ x -1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
y
(+ x -1/2)
(+.f64 x #s(literal -1/2 binary64))
x
-1/2
#s(literal -1/2 binary64)
(/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x))) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000))))
(/.f64 (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))
(- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x)))
(-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))
775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000
#s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64)
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
(+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000)))
(+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))
844448027808355901771309036929/1000000000000000000000000000000
#s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64)
(* x (+ x 918938533204673/1000000000000000))
(*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))
(+ x 918938533204673/1000000000000000)
(+.f64 x #s(literal 918938533204673/1000000000000000 binary64))
918938533204673/1000000000000000
#s(literal 918938533204673/1000000000000000 binary64)
(- 918938533204673/1000000000000000 x)
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* x (+ y -1))
(*.f64 x (+.f64 y #s(literal -1 binary64)))
(+ y -1)
(+.f64 y #s(literal -1 binary64))
-1
#s(literal -1 binary64)
(* y (- x 1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(- x 1/2)
(+.f64 x #s(literal -1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ (* y -1/2) 918938533204673/1000000000000000)
(+.f64 #s(literal 918938533204673/1000000000000000 binary64) (*.f64 y #s(literal -1/2 binary64)))
(* y -1/2)
(*.f64 y #s(literal -1/2 binary64))

Results

158.0ms

256×

valid

Compiler

Compiled 121 to 69 computations (43% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-mult: 20.0ms (37.5% of total)

ival-add: 19.0ms (35.6% of total)

ival-sub: 7.0ms (13.1% of total)

const: 4.0ms (7.5% of total)

ival-div: 3.0ms (5.6% of total)

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

series28.0ms (0.3%)

Counts

13 → 204

Calls

Call 1

Inputs
#<alt (/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x))) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000))))>
#<alt (* x (* x x))>
#<alt (* x (+ x 918938533204673/1000000000000000))>
#<alt (* y (+ x -1/2))>
#<alt (- 918938533204673/1000000000000000 x)>
#<alt (* x (+ y -1))>
#<alt (+ y -1)>
#<alt (* y (- x 1/2))>
#<alt (- x 1/2)>
#<alt (+ (* y -1/2) 918938533204673/1000000000000000)>
#<alt (* y -1/2)>
#<alt (+ (* y (+ x -1/2)) (/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x))) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000)))))>
#<alt (+ x -1/2)>

Outputs
#<alt 918938533204673/1000000000000000>
#<alt (+ 918938533204673/1000000000000000 (* -1 x))>
#<alt (+ 918938533204673/1000000000000000 (* -1 x))>
#<alt (+ 918938533204673/1000000000000000 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))>
#<alt (* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))>
#<alt (* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (* 918938533204673/1000000000000000 x)>
#<alt (* x (+ 918938533204673/1000000000000000 x))>
#<alt (* x (+ 918938533204673/1000000000000000 x))>
#<alt (* x (+ 918938533204673/1000000000000000 x))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 y) (* x y))>
#<alt (+ (* -1/2 y) (* x y))>
#<alt (+ (* -1/2 y) (* x y))>
#<alt (* x y)>
#<alt (* x (+ y (* -1/2 (/ y x))))>
#<alt (* x (+ y (* -1/2 (/ y x))))>
#<alt (* x (+ y (* -1/2 (/ y x))))>
#<alt (* x y)>
#<alt (* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))>
#<alt 918938533204673/1000000000000000>
#<alt (+ 918938533204673/1000000000000000 (* -1 x))>
#<alt (+ 918938533204673/1000000000000000 (* -1 x))>
#<alt (+ 918938533204673/1000000000000000 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))>
#<alt (* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))>
#<alt (* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* x (- y 1))>
#<alt (* x (- y 1))>
#<alt (* x (- y 1))>
#<alt (* x (- y 1))>
#<alt (* x (- y 1))>
#<alt (* x (- y 1))>
#<alt (* x (- y 1))>
#<alt (* x (- y 1))>
#<alt (* x (- y 1))>
#<alt (* x (- y 1))>
#<alt (* x (- y 1))>
#<alt (* x (- y 1))>
#<alt (* -1 x)>
#<alt (+ (* -1 x) (* x y))>
#<alt (+ (* -1 x) (* x y))>
#<alt (+ (* -1 x) (* x y))>
#<alt (* x y)>
#<alt (* y (+ x (* -1 (/ x y))))>
#<alt (* y (+ x (* -1 (/ x y))))>
#<alt (* y (+ x (* -1 (/ x y))))>
#<alt (* x y)>
#<alt (* -1 (* y (+ (* -1 x) (/ x y))))>
#<alt (* -1 (* y (+ (* -1 x) (/ x y))))>
#<alt (* -1 (* y (+ (* -1 x) (/ x y))))>
#<alt -1>
#<alt (- y 1)>
#<alt (- y 1)>
#<alt (- y 1)>
#<alt y>
#<alt (* y (- 1 (/ 1 y)))>
#<alt (* y (- 1 (/ 1 y)))>
#<alt (* y (- 1 (/ 1 y)))>
#<alt y>
#<alt (* -1 (* y (- (/ 1 y) 1)))>
#<alt (* -1 (* y (- (/ 1 y) 1)))>
#<alt (* -1 (* y (- (/ 1 y) 1)))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 y) (* x y))>
#<alt (+ (* -1/2 y) (* x y))>
#<alt (+ (* -1/2 y) (* x y))>
#<alt (* x y)>
#<alt (* x (+ y (* -1/2 (/ y x))))>
#<alt (* x (+ y (* -1/2 (/ y x))))>
#<alt (* x (+ y (* -1/2 (/ y x))))>
#<alt (* x y)>
#<alt (* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))>
#<alt -1/2>
#<alt (- x 1/2)>
#<alt (- x 1/2)>
#<alt (- x 1/2)>
#<alt x>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt 918938533204673/1000000000000000>
#<alt (+ 918938533204673/1000000000000000 (* -1/2 y))>
#<alt (+ 918938533204673/1000000000000000 (* -1/2 y))>
#<alt (+ 918938533204673/1000000000000000 (* -1/2 y))>
#<alt (* -1/2 y)>
#<alt (* y (- (* 918938533204673/1000000000000000 (/ 1 y)) 1/2))>
#<alt (* y (- (* 918938533204673/1000000000000000 (/ 1 y)) 1/2))>
#<alt (* y (- (* 918938533204673/1000000000000000 (/ 1 y)) 1/2))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (- 1/2 (* 918938533204673/1000000000000000 (/ 1 y)))))>
#<alt (* -1 (* y (- 1/2 (* 918938533204673/1000000000000000 (/ 1 y)))))>
#<alt (* -1 (* y (- 1/2 (* 918938533204673/1000000000000000 (/ 1 y)))))>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) (/ (pow x 3) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))))>
#<alt (- (+ (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) (* y (- x 1/2))) (/ (pow x 3) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))))>
#<alt (- (+ (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) (* y (- x 1/2))) (/ (pow x 3) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))))>
#<alt (- (+ (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) (* y (- x 1/2))) (/ (pow x 3) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))))>
#<alt (* y (- x 1/2))>
#<alt (* y (- (+ x (/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))))) (+ 1/2 (/ (pow x 3) (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))))))>
#<alt (* y (- (+ x (/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))))) (+ 1/2 (/ (pow x 3) (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))))))>
#<alt (* y (- (+ x (/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))))) (+ 1/2 (/ (pow x 3) (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))))))>
#<alt (* y (- x 1/2))>
#<alt (* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) (/ (pow x 3) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) y)))))>
#<alt (* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) (/ (pow x 3) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) y)))))>
#<alt (* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) (/ (pow x 3) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) y)))))>
#<alt (+ 918938533204673/1000000000000000 (* -1/2 y))>
#<alt (+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))>
#<alt (+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))>
#<alt (+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))>
#<alt (* x (- y 1))>
#<alt (* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))>
#<alt (* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))>
#<alt (* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))>
#<alt (* -1 (* x (+ 1 (* -1 y))))>
#<alt (* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))>
#<alt -1/2>
#<alt (- x 1/2)>
#<alt (- x 1/2)>
#<alt (- x 1/2)>
#<alt x>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>

Calls

51 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x))) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000))))
1.0ms	y	@	0	(+ (* y (+ x -1/2)) (/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x))) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000)))))
1.0ms	y	@	-inf	(* x (+ y -1))
1.0ms	x	@	inf	(+ x -1/2)
1.0ms	x	@	0	(+ (* y (+ x -1/2)) (/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x))) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000)))))

rewrite726.0ms (6.8%)

Algorithm

1×	batch-egg-rewrite

Rules

4630×	`/-lowering-/.f32`
4630×	`/-lowering-/.f64`
4006×	`-lowering-.f32`
4006×	`-lowering-.f64`
3634×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	55
1	168	55
2	1406	55
0	8167	53

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 806

Calls

Call 1

Inputs
(/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x))) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000))))
(* x (* x x))
(* x (+ x 918938533204673/1000000000000000))
(* y (+ x -1/2))
(- 918938533204673/1000000000000000 x)
(* x (+ y -1))
(+ y -1)
(* y (- x 1/2))
(- x 1/2)
(+ (* y -1/2) 918938533204673/1000000000000000)
(* y -1/2)
(+ (* y (+ x -1/2)) (/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x))) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000)))))
(+ x -1/2)

Outputs
(+.f64 #s(literal 918938533204673/1000000000000000 binary64) (neg.f64 x))
(+.f64 (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))) (neg.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))))
(+.f64 (neg.f64 x) #s(literal 918938533204673/1000000000000000 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))) #s(literal -1 binary64)))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(-.f64 (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))) (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))))
(-.f64 (/.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))) (/.f64 (*.f64 x x) (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))
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(/.f64 (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (pow.f64 (+.f64 (neg.f64 x) (.f64 y (+.f64 x #s(literal -1/2 binary64)))) #s(literal 3 binary64))) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (-.f64 (.f64 (+.f64 (neg.f64 x) (.f64 y (+.f64 x #s(literal -1/2 binary64)))) (+.f64 (neg.f64 x) (.f64 y (+.f64 x #s(literal -1/2 binary64))))) (.f64 #s(literal 918938533204673/1000000000000000 binary64) (+.f64 (neg.f64 x) (.f64 y (+.f64 x #s(literal -1/2 binary64))))))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (pow.f64 (+.f64 (.f64 y #s(literal -1/2 binary64)) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (-.f64 (.f64 (+.f64 (.f64 y #s(literal -1/2 binary64)) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)) (+.f64 (.f64 y #s(literal -1/2 binary64)) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))) (.f64 (.f64 x y) (+.f64 (*.f64 y #s(literal -1/2 binary64)) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))))))
(/.f64 (+.f64 (pow.f64 (+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (.f64 x y)) #s(literal 3 binary64)) (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y)))) (+.f64 (.f64 (+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (.f64 x y)) (+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (.f64 x y))) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 (+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (.f64 x y)) (.f64 y #s(literal -1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) #s(literal 918938533204673/1000000000000000 binary64)) #s(literal 3 binary64)) (.f64 (.f64 (neg.f64 x) x) x)) (+.f64 (.f64 (+.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) #s(literal 918938533204673/1000000000000000 binary64)) (+.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) #s(literal 918938533204673/1000000000000000 binary64))) (-.f64 (.f64 x x) (.f64 (+.f64 (*.f64 y (+.f64 x #s(literal -1/2 binary64))) #s(literal 918938533204673/1000000000000000 binary64)) (neg.f64 x)))))
(pow.f64 (/.f64 (+.f64 (.f64 (.f64 y y) (.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64)))) (.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (-.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (.f64 y (+.f64 x #s(literal -1/2 binary64)))))) (+.f64 (.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (.f64 (.f64 y y) (.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64))))) (.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (-.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) #s(literal 918938533204673/1000000000000000 binary64)) x) (-.f64 (.f64 (.f64 y y) (.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64)))) (*.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (.f64 (.f64 y y) (.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64))))) (.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 y y) (.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64)))) (.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (-.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))))))
(.f64 (-.f64 (.f64 (.f64 y y) (.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64)))) (.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) #s(literal 918938533204673/1000000000000000 binary64)) x)))
(+.f64 x #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) x)
(-.f64 x #s(literal 1/2 binary64))
(-.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/8 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/2 binary64))))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (+.f64 x #s(literal 1/2 binary64))))
(-.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))))) (/.f64 #s(literal 1/8 binary64) (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))))))
(-.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x x) (.f64 x #s(literal -1/2 binary64))))) (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x x) (.f64 x #s(literal -1/2 binary64))))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal -1/2 binary64) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/2 binary64)))) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 x x) #s(literal -1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/2 binary64)))) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 x x) #s(literal -1/4 binary64))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (+.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x x) (.f64 x #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (*.f64 x x) #s(literal -1/4 binary64)) (+.f64 x #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (neg.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (neg.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x x) (.f64 x #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (+.f64 (*.f64 x x) #s(literal -1/4 binary64))) (neg.f64 (+.f64 x #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 #s(literal -1/2 binary64) x))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/2 binary64))))) (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(literal 1/8 binary64))) (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/2 binary64)))) (+.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x #s(literal 1/2 binary64))) (.f64 (+.f64 x #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (+.f64 x #s(literal 1/2 binary64)) (+.f64 x #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)))) (neg.f64 (neg.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)))) (neg.f64 (neg.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (*.f64 x x) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (+.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal -1/2 binary64) x)))
(pow.f64 (/.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/2 binary64)))) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 x x) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(.f64 (+.f64 (.f64 x x) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1/2 binary64))))

simplify872.0ms (8.2%)

Algorithm

1×	egg-herbie

Rules

10704×	`accelerator-lowering-fma.f32`
10704×	`accelerator-lowering-fma.f64`
3116×	`-lowering-.f32`
3116×	`-lowering-.f64`
2204×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	1079
1	321	1061
2	911	1043
3	2602	1043
4	7509	1043
0	8184	995

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
918938533204673/1000000000000000
(+ 918938533204673/1000000000000000 (* -1 x))
(+ 918938533204673/1000000000000000 (* -1 x))
(+ 918938533204673/1000000000000000 (* -1 x))
(* -1 x)
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(* -1 x)
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 918938533204673/1000000000000000 x)
(* x (+ 918938533204673/1000000000000000 x))
(* x (+ 918938533204673/1000000000000000 x))
(* x (+ 918938533204673/1000000000000000 x))
(pow x 2)
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(pow x 2)
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* -1/2 y)
(+ (* -1/2 y) (* x y))
(+ (* -1/2 y) (* x y))
(+ (* -1/2 y) (* x y))
(* x y)
(* x (+ y (* -1/2 (/ y x))))
(* x (+ y (* -1/2 (/ y x))))
(* x (+ y (* -1/2 (/ y x))))
(* x y)
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
918938533204673/1000000000000000
(+ 918938533204673/1000000000000000 (* -1 x))
(+ 918938533204673/1000000000000000 (* -1 x))
(+ 918938533204673/1000000000000000 (* -1 x))
(* -1 x)
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(* -1 x)
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(* x (- y 1))
(* x (- y 1))
(* x (- y 1))
(* x (- y 1))
(* x (- y 1))
(* x (- y 1))
(* x (- y 1))
(* x (- y 1))
(* x (- y 1))
(* x (- y 1))
(* x (- y 1))
(* x (- y 1))
(* -1 x)
(+ (* -1 x) (* x y))
(+ (* -1 x) (* x y))
(+ (* -1 x) (* x y))
(* x y)
(* y (+ x (* -1 (/ x y))))
(* y (+ x (* -1 (/ x y))))
(* y (+ x (* -1 (/ x y))))
(* x y)
(* -1 (* y (+ (* -1 x) (/ x y))))
(* -1 (* y (+ (* -1 x) (/ x y))))
(* -1 (* y (+ (* -1 x) (/ x y))))
-1
(- y 1)
(- y 1)
(- y 1)
y
(* y (- 1 (/ 1 y)))
(* y (- 1 (/ 1 y)))
(* y (- 1 (/ 1 y)))
y
(* -1 (* y (- (/ 1 y) 1)))
(* -1 (* y (- (/ 1 y) 1)))
(* -1 (* y (- (/ 1 y) 1)))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* -1/2 y)
(+ (* -1/2 y) (* x y))
(+ (* -1/2 y) (* x y))
(+ (* -1/2 y) (* x y))
(* x y)
(* x (+ y (* -1/2 (/ y x))))
(* x (+ y (* -1/2 (/ y x))))
(* x (+ y (* -1/2 (/ y x))))
(* x y)
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
-1/2
(- x 1/2)
(- x 1/2)
(- x 1/2)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (- 1 (* 1/2 (/ 1 x))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
918938533204673/1000000000000000
(+ 918938533204673/1000000000000000 (* -1/2 y))
(+ 918938533204673/1000000000000000 (* -1/2 y))
(+ 918938533204673/1000000000000000 (* -1/2 y))
(* -1/2 y)
(* y (- (* 918938533204673/1000000000000000 (/ 1 y)) 1/2))
(* y (- (* 918938533204673/1000000000000000 (/ 1 y)) 1/2))
(* y (- (* 918938533204673/1000000000000000 (/ 1 y)) 1/2))
(* -1/2 y)
(* -1 (* y (- 1/2 (* 918938533204673/1000000000000000 (/ 1 y)))))
(* -1 (* y (- 1/2 (* 918938533204673/1000000000000000 (/ 1 y)))))
(* -1 (* y (- 1/2 (* 918938533204673/1000000000000000 (/ 1 y)))))
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) (/ (pow x 3) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))))
(- (+ (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) (* y (- x 1/2))) (/ (pow x 3) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))))
(- (+ (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) (* y (- x 1/2))) (/ (pow x 3) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))))
(- (+ (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) (* y (- x 1/2))) (/ (pow x 3) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))))
(* y (- x 1/2))
(* y (- (+ x (/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))))) (+ 1/2 (/ (pow x 3) (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))))))
(* y (- (+ x (/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))))) (+ 1/2 (/ (pow x 3) (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))))))
(* y (- (+ x (/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))))) (+ 1/2 (/ (pow x 3) (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))))))
(* y (- x 1/2))
(* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) (/ (pow x 3) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) y)))))
(* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) (/ (pow x 3) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) y)))))
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Outputs
918938533204673/1000000000000000
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918938533204673/1000000000000000
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918938533204673/1000000000000000
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(* y (- (+ x (/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))))) (+ 1/2 (/ (pow x 3) (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))))))
(+.f64 (+.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 (.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x)) #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64)))) (/.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal -844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x)))))
(* y (- (+ x (/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))))) (+ 1/2 (/ (pow x 3) (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))))))
(+.f64 (+.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 (.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x)) #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64)))) (/.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal -844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x)))))
(* y (- (+ x (/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))))) (+ 1/2 (/ (pow x 3) (* y (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))))))
(+.f64 (+.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 (.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x)) #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64)))) (/.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal -844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x)))))
(* y (- x 1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) (/ (pow x 3) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) y)))))
(+.f64 (+.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 (.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x)) #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64)))) (/.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal -844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x)))))
(* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) (/ (pow x 3) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) y)))))
(+.f64 (+.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 (.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x)) #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64)))) (/.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal -844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x)))))
(* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) (/ (pow x 3) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x))))) y)))))
(+.f64 (+.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 (.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x)) #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64)))) (/.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal -844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x)))))
(+ 918938533204673/1000000000000000 (* -1/2 y))
(+.f64 #s(literal 918938533204673/1000000000000000 binary64) (*.f64 y #s(literal -1/2 binary64)))
(+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* x (- y 1))
(*.f64 x (+.f64 #s(literal -1 binary64) y))
(* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* -1 (* x (+ 1 (* -1 y))))
(*.f64 x (+.f64 #s(literal -1 binary64) y))
(* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
-1/2
#s(literal -1/2 binary64)
(- x 1/2)
(+.f64 x #s(literal -1/2 binary64))
(- x 1/2)
(+.f64 x #s(literal -1/2 binary64))
(- x 1/2)
(+.f64 x #s(literal -1/2 binary64))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/2 binary64))

eval428.0ms (4%)

Compiler: Compiled 41830 to 22593 computations (46% saved)

prune160.0ms (1.5%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	1006	4	1010
Fresh	0	1	1
Picked	1	4	5
Done	0	0	0
Total	1007	9	1016

Accuracy

100.0%

Counts

1016 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.0%	(fma.f64 (.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (.f64 y (+.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 y (+.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
▶	37.3%	(/.f64 (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))
✓	54.3%	(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
✓	51.4%	(+.f64 (*.f64 y #s(literal -1/2 binary64)) #s(literal 918938533204673/1000000000000000 binary64))
✓	47.3%	(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
▶	25.2%	(*.f64 y x)
▶	24.1%	(*.f64 y #s(literal -1/2 binary64))
✓	49.7%	(*.f64 x (+.f64 y #s(literal -1 binary64)))
▶	29.0%	#s(literal 918938533204673/1000000000000000 binary64)

Compiler

Compiled 134 to 98 computations (26.9% saved)

localize523.0ms (4.9%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	0	(-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))
✓	cost-diff	0	(*.f64 y x)
✓	cost-diff	0	(*.f64 y #s(literal -1/2 binary64))
✓	cost-diff	0	(+.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
✓	cost-diff	0	(.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	7168	(fma.f64 (.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (.f64 y (+.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 y (+.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
✓	accuracy	100.0%	(+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))
✓	accuracy	100.0%	(*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	65.8%	(/.f64 (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))
✓	accuracy	100.0%	(*.f64 y x)
✓	accuracy	100.0%	(*.f64 y #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
✓	accuracy	99.9%	(.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
✓	accuracy	67.9%	(fma.f64 (.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (.f64 y (+.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 y (+.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))

Rules

3138×	`accelerator-lowering-fma.f32`
3138×	`accelerator-lowering-fma.f64`
3000×	`-lowering-.f32`
3000×	`-lowering-.f64`
1928×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	113
1	75	101
2	212	99
3	937	99
4	7504	99
0	8295	96

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (* (* (* y (+ x -1/2)) (* y (+ x 1/2))) (/ 1 (* y (+ x 1/2)))) (- 918938533204673/1000000000000000 x))
(* (* y (+ x -1/2)) (* y (+ x 1/2)))
(* y (+ x -1/2))
y
(+ x -1/2)
x
-1/2
(* y (+ x 1/2))
(+ x 1/2)
1/2
(/ 1 (* y (+ x 1/2)))
1
(- 918938533204673/1000000000000000 x)
918938533204673/1000000000000000
(* y -1/2)
(* y x)
(/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x))) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000))))
(- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x)))
775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000
(* x (* x x))
(* x x)
(+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000)))
844448027808355901771309036929/1000000000000000000000000000000
(* x (+ x 918938533204673/1000000000000000))
(+ x 918938533204673/1000000000000000)

Outputs
(+ (* (* (* y (+ x -1/2)) (* y (+ x 1/2))) (/ 1 (* y (+ x 1/2)))) (- 918938533204673/1000000000000000 x))
(+.f64 (*.f64 y (+.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* (* y (+ x -1/2)) (* y (+ x 1/2)))
(.f64 y (.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 y (+.f64 x #s(literal 1/2 binary64)))))
(* y (+ x -1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
y
(+ x -1/2)
(+.f64 x #s(literal -1/2 binary64))
x
-1/2
#s(literal -1/2 binary64)
(* y (+ x 1/2))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(+ x 1/2)
(+.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(/ 1 (* y (+ x 1/2)))
(/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(- 918938533204673/1000000000000000 x)
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
918938533204673/1000000000000000
#s(literal 918938533204673/1000000000000000 binary64)
(* y -1/2)
(*.f64 y #s(literal -1/2 binary64))
(* y x)
(*.f64 y x)
(/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x))) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000))))
(/.f64 (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))
(- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x)))
(-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))
775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000
#s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64)
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
(+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000)))
(+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))
844448027808355901771309036929/1000000000000000000000000000000
#s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64)
(* x (+ x 918938533204673/1000000000000000))
(*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))
(+ x 918938533204673/1000000000000000)
(+.f64 x #s(literal 918938533204673/1000000000000000 binary64))

Results

110.0ms

256×

valid

Compiler

Compiled 128 to 76 computations (40.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-mult: 29.0ms (41.7% of total)

ival-add: 23.0ms (33.1% of total)

ival-div: 5.0ms (7.2% of total)

ival-sub: 5.0ms (7.2% of total)

const: 4.0ms (5.7% of total)

<compiled-spec>: 3.0ms (4.3% of total)

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

series33.0ms (0.3%)

Counts

14 → 240

Calls

Call 1

Inputs
#<alt (+ (* (* (* y (+ x -1/2)) (* y (+ x 1/2))) (/ 1 (* y (+ x 1/2)))) (- 918938533204673/1000000000000000 x))>
#<alt (/ 1 (* y (+ x 1/2)))>
#<alt (* (* y (+ x -1/2)) (* y (+ x 1/2)))>
#<alt (* y (+ x 1/2))>
#<alt (* y -1/2)>
#<alt (* y x)>
#<alt (/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x))) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000))))>
#<alt (* x (* x x))>
#<alt (* x (+ x 918938533204673/1000000000000000))>
#<alt (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000)))>
#<alt (* y (+ x -1/2))>
#<alt (+ x -1/2)>
#<alt (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x)))>
#<alt (* x x)>

Outputs
#<alt (- 918938533204673/1000000000000000 x)>
#<alt (- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)>
#<alt (- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)>
#<alt (- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)>
#<alt (* y (- x 1/2))>
#<alt (* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))>
#<alt (* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))>
#<alt (* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))>
#<alt (* y (- x 1/2))>
#<alt (* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))>
#<alt (* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))>
#<alt (* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))>
#<alt (+ 918938533204673/1000000000000000 (* -1/2 y))>
#<alt (+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))>
#<alt (+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))>
#<alt (+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))>
#<alt (* x (- y 1))>
#<alt (* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))>
#<alt (* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))>
#<alt (* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))>
#<alt (* -1 (* x (+ 1 (* -1 y))))>
#<alt (* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 2 y)>
#<alt (+ (* -4 (/ x y)) (* 2 (/ 1 y)))>
#<alt (+ (* x (- (* 8 (/ x y)) (* 4 (/ 1 y)))) (* 2 (/ 1 y)))>
#<alt (+ (* x (- (* x (+ (* -16 (/ x y)) (* 8 (/ 1 y)))) (* 4 (/ 1 y)))) (* 2 (/ 1 y)))>
#<alt (/ 1 (* x y))>
#<alt (/ (- (/ 1 y) (* 1/2 (/ 1 (* x y)))) x)>
#<alt (/ (- (+ (/ 1/4 (* (pow x 2) y)) (/ 1 y)) (/ 1/2 (* x y))) x)>
#<alt (/ (- (+ (/ 1 y) (* 1/4 (/ 1 (* (pow x 2) y)))) (+ (/ 1/2 (* x y)) (* 1/8 (/ 1 (* (pow x 3) y))))) x)>
#<alt (/ 1 (* x y))>
#<alt (* -1 (/ (- (* 1/2 (/ 1 (* x y))) (/ 1 y)) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 (* x y))) (* 1/2 (/ 1 y))) x)) (/ 1 y)) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* x y))) (* 1/4 (/ 1 y))) x)) (* 1/2 (/ 1 y))) x)) (/ 1 y)) x))>
#<alt (* (pow y 2) (* (+ 1/2 x) (- x 1/2)))>
#<alt (* (pow y 2) (* (+ 1/2 x) (- x 1/2)))>
#<alt (* (pow y 2) (* (+ 1/2 x) (- x 1/2)))>
#<alt (* (pow y 2) (* (+ 1/2 x) (- x 1/2)))>
#<alt (* (pow y 2) (* (+ 1/2 x) (- x 1/2)))>
#<alt (* (pow y 2) (* (+ 1/2 x) (- x 1/2)))>
#<alt (* (pow y 2) (* (+ 1/2 x) (- x 1/2)))>
#<alt (* (pow y 2) (* (+ 1/2 x) (- x 1/2)))>
#<alt (* (pow y 2) (* (+ 1/2 x) (- x 1/2)))>
#<alt (* (pow y 2) (* (+ 1/2 x) (- x 1/2)))>
#<alt (* (pow y 2) (* (+ 1/2 x) (- x 1/2)))>
#<alt (* (pow y 2) (* (+ 1/2 x) (- x 1/2)))>
#<alt (* -1/4 (pow y 2))>
#<alt (+ (* -1/4 (pow y 2)) (* (pow x 2) (pow y 2)))>
#<alt (+ (* -1/4 (pow y 2)) (* (pow x 2) (pow y 2)))>
#<alt (+ (* -1/4 (pow y 2)) (* (pow x 2) (pow y 2)))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))>
#<alt (* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))>
#<alt (* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))>
#<alt (* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))>
#<alt (* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* 1/2 y)>
#<alt (+ (* 1/2 y) (* x y))>
#<alt (+ (* 1/2 y) (* x y))>
#<alt (+ (* 1/2 y) (* x y))>
#<alt (* x y)>
#<alt (* x (+ y (* 1/2 (/ y x))))>
#<alt (* x (+ y (* 1/2 (/ y x))))>
#<alt (* x (+ y (* 1/2 (/ y x))))>
#<alt (* x y)>
#<alt (* -1 (* x (+ (* -1 y) (* -1/2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* -1/2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* -1/2 (/ y x)))))>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* -1/2 y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt 918938533204673/1000000000000000>
#<alt (+ 918938533204673/1000000000000000 (* -1 x))>
#<alt (+ 918938533204673/1000000000000000 (* -1 x))>
#<alt (+ 918938533204673/1000000000000000 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))>
#<alt (* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))>
#<alt (* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (* 918938533204673/1000000000000000 x)>
#<alt (* x (+ 918938533204673/1000000000000000 x))>
#<alt (* x (+ 918938533204673/1000000000000000 x))>
#<alt (* x (+ 918938533204673/1000000000000000 x))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt 844448027808355901771309036929/1000000000000000000000000000000>
#<alt (+ 844448027808355901771309036929/1000000000000000000000000000000 (* 918938533204673/1000000000000000 x))>
#<alt (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))>
#<alt (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* y (- x 1/2))>
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 y) (* x y))>
#<alt (+ (* -1/2 y) (* x y))>
#<alt (+ (* -1/2 y) (* x y))>
#<alt (* x y)>
#<alt (* x (+ y (* -1/2 (/ y x))))>
#<alt (* x (+ y (* -1/2 (/ y x))))>
#<alt (* x (+ y (* -1/2 (/ y x))))>
#<alt (* x y)>
#<alt (* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))>
#<alt -1/2>
#<alt (- x 1/2)>
#<alt (- x 1/2)>
#<alt (- x 1/2)>
#<alt x>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000>
#<alt (+ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* -1 (pow x 3)))>
#<alt (+ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* -1 (pow x 3)))>
#<alt (+ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* -1 (pow x 3)))>
#<alt (* -1 (pow x 3))>
#<alt (* (pow x 3) (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))) 1))>
#<alt (* (pow x 3) (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))) 1))>
#<alt (* (pow x 3) (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))) 1))>
#<alt (* -1 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1 (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow x 3) (- 1 (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow x 3) (- 1 (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

60 calls:

Time	Variable		Point	Expression
9.0ms	y	@	-inf	(* y (+ x 1/2))
3.0ms	x	@	-inf	(/ 1 (* y (+ x 1/2)))
1.0ms	y	@	0	(/ 1 (* y (+ x 1/2)))
1.0ms	y	@	0	(* (* y (+ x -1/2)) (* y (+ x 1/2)))
1.0ms	x	@	-inf	(* (* y (+ x -1/2)) (* y (+ x 1/2)))

rewrite656.0ms (6.1%)

Algorithm

1×	batch-egg-rewrite

Rules

4922×	`-lowering-.f32`
4922×	`-lowering-.f64`
4796×	`/-lowering-/.f32`
4796×	`/-lowering-/.f64`
2978×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	84
1	168	74
2	1537	74
0	8602	72

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 771

Calls

Call 1

Inputs
(+ (* (* (* y (+ x -1/2)) (* y (+ x 1/2))) (/ 1 (* y (+ x 1/2)))) (- 918938533204673/1000000000000000 x))
(/ 1 (* y (+ x 1/2)))
(* (* y (+ x -1/2)) (* y (+ x 1/2)))
(* y (+ x 1/2))
(* y -1/2)
(* y x)
(/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x))) (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000))))
(* x (* x x))
(* x (+ x 918938533204673/1000000000000000))
(+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000)))
(* y (+ x -1/2))
(+ x -1/2)
(- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* x (* x x)))
(* x x)

Outputs
(+.f64 (.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y #s(literal 1 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(+.f64 #s(literal 918938533204673/1000000000000000 binary64) (+.f64 (neg.f64 x) (.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y #s(literal 1 binary64)))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y #s(literal 1 binary64))))
(+.f64 (+.f64 (.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y #s(literal 1 binary64))) #s(literal 918938533204673/1000000000000000 binary64)) (neg.f64 x))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) (-.f64 x (.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))) (-.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))) (.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y #s(literal 1 binary64)))))
(-.f64 (+.f64 (.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y #s(literal 1 binary64))) #s(literal 918938533204673/1000000000000000 binary64)) x)
(-.f64 (/.f64 (.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y #s(literal 1 binary64)))) (-.f64 (.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y #s(literal 1 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))) (/.f64 (.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)) (-.f64 (.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 y #s(literal 1 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))))
(-.f64 (+.f64 (.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y #s(literal 1 binary64))) (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))) (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))))
(fma.f64 y (*.f64 (+.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 y (.f64 (.f64 (.f64 y (+.f64 x #s(literal 1/2 binary64))) (+.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 y (+.f64 x #s(literal 1/2 binary64))))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 y (/.f64 (.f64 (.f64 y (+.f64 x #s(literal 1/2 binary64))) (+.f64 x #s(literal -1/2 binary64))) (*.f64 y (+.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 (*.f64 y (+.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 (.f64 y (+.f64 x #s(literal 1/2 binary64))) (.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 y (+.f64 x #s(literal 1/2 binary64))))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 (.f64 y (+.f64 x #s(literal 1/2 binary64))) (/.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (*.f64 y (+.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 (.f64 y (.f64 (.f64 y (+.f64 x #s(literal 1/2 binary64))) (+.f64 x #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 y (+.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y #s(literal 1 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y #s(literal 1 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 y (+.f64 x #s(literal 1/2 binary64)))) (.f64 y (.f64 (.f64 y (+.f64 x #s(literal 1/2 binary64))) (+.f64 x #s(literal -1/2 binary64)))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))) (.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 y #s(literal 1 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))) #s(literal -844448027808355901771309036929/1000000000000000000000000000000 binary64))) (.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 y #s(literal 1 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))) (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 y #s(literal 1 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 y #s(literal 1 binary64))))
(fma.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 y #s(literal 1 binary64)) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 (-.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))) (.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 y #s(literal 1 binary64))))
(fma.f64 (.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y y)) (.f64 (+.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 y (+.f64 x #s(literal 1/2 binary64))))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 (.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y y)) (/.f64 (+.f64 x #s(literal 1/2 binary64)) (*.f64 y (+.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 (/.f64 y y) (/.f64 (.f64 (.f64 y (+.f64 x #s(literal 1/2 binary64))) (+.f64 x #s(literal -1/2 binary64))) (+.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 (/.f64 y (+.f64 x #s(literal 1/2 binary64))) (/.f64 (.f64 (.f64 y (+.f64 x #s(literal 1/2 binary64))) (+.f64 x #s(literal -1/2 binary64))) y) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 (/.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) y) (/.f64 (.f64 y (+.f64 x #s(literal 1/2 binary64))) (+.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 (/.f64 (.f64 y (+.f64 x #s(literal 1/2 binary64))) (+.f64 x #s(literal 1/2 binary64))) (/.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) y) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 (/.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (+.f64 x #s(literal 1/2 binary64))) (/.f64 (.f64 y (+.f64 x #s(literal 1/2 binary64))) y) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
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(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x #s(literal -1/2 binary64))) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 x x) #s(literal -1/4 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x #s(literal -1/2 binary64))) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 x x) #s(literal -1/4 binary64)))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (-.f64 (+.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x #s(literal -1/2 binary64))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x x) (.f64 x #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (*.f64 x x) #s(literal -1/4 binary64)) (+.f64 x #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (+.f64 (*.f64 x x) #s(literal -1/4 binary64))) (neg.f64 (+.f64 x #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (neg.f64 (-.f64 (+.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x x) (.f64 x #s(literal -1/2 binary64))))))
(/.f64 (-.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (+.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 #s(literal -1/2 binary64) x))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x #s(literal 1/2 binary64))) (.f64 (+.f64 x #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (+.f64 x #s(literal 1/2 binary64)) (+.f64 x #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (*.f64 x x) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (+.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal -1/2 binary64) x)))
(/.f64 (neg.f64 (-.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (neg.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)))) (neg.f64 (neg.f64 (-.f64 (+.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x #s(literal -1/2 binary64))))))
(pow.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x #s(literal -1/2 binary64))) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 x x) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (.f64 x x) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/2 binary64)))))
(.f64 (+.f64 (.f64 x x) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1/2 binary64))))
(+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x x) (neg.f64 x)))
(+.f64 (.f64 (.f64 x x) (neg.f64 x)) #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64))
(-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))
(-.f64 (/.f64 #s(literal 467281046507231535557839844855961690659155326809117752385379341233607442881727175514780123368029846518396839376786774913239842372741313/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))))) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))))))
(-.f64 (/.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 x (neg.f64 (*.f64 x x)) #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64))
(fma.f64 (*.f64 x x) (neg.f64 x) #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64))
(fma.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)) #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64))
(fma.f64 (neg.f64 x) (*.f64 x x) #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64))
(fma.f64 (neg.f64 (*.f64 x x)) x #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64))
(fma.f64 (*.f64 (neg.f64 x) x) x #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))))) (-.f64 #s(literal 467281046507231535557839844855961690659155326809117752385379341233607442881727175514780123368029846518396839376786774913239842372741313/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))))) (-.f64 #s(literal 467281046507231535557839844855961690659155326809117752385379341233607442881727175514780123368029846518396839376786774913239842372741313/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x)))))))
(/.f64 (-.f64 #s(literal 467281046507231535557839844855961690659155326809117752385379341233607442881727175514780123368029846518396839376786774913239842372741313/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (*.f64 x x))))))
(/.f64 (-.f64 #s(literal 467281046507231535557839844855961690659155326809117752385379341233607442881727175514780123368029846518396839376786774913239842372741313/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x x) (neg.f64 x))))))
(/.f64 (-.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (*.f64 x x))))
(/.f64 (-.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 (*.f64 x x) (neg.f64 x))))
(/.f64 (neg.f64 (-.f64 #s(literal 467281046507231535557839844855961690659155326809117752385379341233607442881727175514780123368029846518396839376786774913239842372741313/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (neg.f64 (+.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (*.f64 x x)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 467281046507231535557839844855961690659155326809117752385379341233607442881727175514780123368029846518396839376786774913239842372741313/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (neg.f64 (+.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x x) (neg.f64 x)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (neg.f64 (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (*.f64 x x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (neg.f64 (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 (*.f64 x x) (neg.f64 x)))))
(/.f64 (-.f64 (.f64 #s(literal 467281046507231535557839844855961690659155326809117752385379341233607442881727175514780123368029846518396839376786774913239842372741313/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))))) (.f64 (+.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (.f64 (+.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (*.f64 x x)))))))
(/.f64 (-.f64 (.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))) (.f64 (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 467281046507231535557839844855961690659155326809117752385379341233607442881727175514780123368029846518396839376786774913239842372741313/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))))) (neg.f64 (neg.f64 (+.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (*.f64 x x))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (neg.f64 (neg.f64 (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (*.f64 x x))))))
(pow.f64 (/.f64 (+.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))))) (-.f64 #s(literal 467281046507231535557839844855961690659155326809117752385379341233607442881727175514780123368029846518396839376786774913239842372741313/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))))) #s(literal -1 binary64))
(.f64 (-.f64 #s(literal 467281046507231535557839844855961690659155326809117752385379341233607442881727175514780123368029846518396839376786774913239842372741313/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))))))
(.f64 (-.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))

simplify642.0ms (6%)

Algorithm

1×	egg-herbie

Rules

8574×	`accelerator-lowering-fma.f32`
8574×	`accelerator-lowering-fma.f64`
3842×	`-lowering-.f32`
3842×	`-lowering-.f64`
2076×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	180	1360
1	550	1345
2	1508	1340
3	4781	1330
0	8300	1285

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
(- 918938533204673/1000000000000000 x)
(- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)
(- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)
(- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)
(* y (- x 1/2))
(* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))
(* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))
(* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))
(* y (- x 1/2))
(* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))
(* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))
(* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))
(+ 918938533204673/1000000000000000 (* -1/2 y))
(+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))
(+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))
(+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))
(* x (- y 1))
(* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))
(* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))
(* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))
(* -1 (* x (+ 1 (* -1 y))))
(* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))
(* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))
(* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))
(/ 1 (* y (+ 1/2 x)))
(/ 1 (* y (+ 1/2 x)))
(/ 1 (* y (+ 1/2 x)))
(/ 1 (* y (+ 1/2 x)))
(/ 1 (* y (+ 1/2 x)))
(/ 1 (* y (+ 1/2 x)))
(/ 1 (* y (+ 1/2 x)))
(/ 1 (* y (+ 1/2 x)))
(/ 1 (* y (+ 1/2 x)))
(/ 1 (* y (+ 1/2 x)))
(/ 1 (* y (+ 1/2 x)))
(/ 1 (* y (+ 1/2 x)))
(/ 2 y)
(+ (* -4 (/ x y)) (* 2 (/ 1 y)))
(+ (* x (- (* 8 (/ x y)) (* 4 (/ 1 y)))) (* 2 (/ 1 y)))
(+ (* x (- (* x (+ (* -16 (/ x y)) (* 8 (/ 1 y)))) (* 4 (/ 1 y)))) (* 2 (/ 1 y)))
(/ 1 (* x y))
(/ (- (/ 1 y) (* 1/2 (/ 1 (* x y)))) x)
(/ (- (+ (/ 1/4 (* (pow x 2) y)) (/ 1 y)) (/ 1/2 (* x y))) x)
(/ (- (+ (/ 1 y) (* 1/4 (/ 1 (* (pow x 2) y)))) (+ (/ 1/2 (* x y)) (* 1/8 (/ 1 (* (pow x 3) y))))) x)
(/ 1 (* x y))
(* -1 (/ (- (* 1/2 (/ 1 (* x y))) (/ 1 y)) x))
(* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 (* x y))) (* 1/2 (/ 1 y))) x)) (/ 1 y)) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* x y))) (* 1/4 (/ 1 y))) x)) (* 1/2 (/ 1 y))) x)) (/ 1 y)) x))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(* -1/4 (pow y 2))
(+ (* -1/4 (pow y 2)) (* (pow x 2) (pow y 2)))
(+ (* -1/4 (pow y 2)) (* (pow x 2) (pow y 2)))
(+ (* -1/4 (pow y 2)) (* (pow x 2) (pow y 2)))
(* (pow x 2) (pow y 2))
(* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))
(* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))
(* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))
(* (pow x 2) (pow y 2))
(* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))
(* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))
(* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))
(* y (+ 1/2 x))
(* y (+ 1/2 x))
(* y (+ 1/2 x))
(* y (+ 1/2 x))
(* y (+ 1/2 x))
(* y (+ 1/2 x))
(* y (+ 1/2 x))
(* y (+ 1/2 x))
(* y (+ 1/2 x))
(* y (+ 1/2 x))
(* y (+ 1/2 x))
(* y (+ 1/2 x))
(* 1/2 y)
(+ (* 1/2 y) (* x y))
(+ (* 1/2 y) (* x y))
(+ (* 1/2 y) (* x y))
(* x y)
(* x (+ y (* 1/2 (/ y x))))
(* x (+ y (* 1/2 (/ y x))))
(* x (+ y (* 1/2 (/ y x))))
(* x y)
(* -1 (* x (+ (* -1 y) (* -1/2 (/ y x)))))
(* -1 (* x (+ (* -1 y) (* -1/2 (/ y x)))))
(* -1 (* x (+ (* -1 y) (* -1/2 (/ y x)))))
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
918938533204673/1000000000000000
(+ 918938533204673/1000000000000000 (* -1 x))
(+ 918938533204673/1000000000000000 (* -1 x))
(+ 918938533204673/1000000000000000 (* -1 x))
(* -1 x)
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(* -1 x)
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 918938533204673/1000000000000000 x)
(* x (+ 918938533204673/1000000000000000 x))
(* x (+ 918938533204673/1000000000000000 x))
(* x (+ 918938533204673/1000000000000000 x))
(pow x 2)
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(pow x 2)
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
844448027808355901771309036929/1000000000000000000000000000000
(+ 844448027808355901771309036929/1000000000000000000000000000000 (* 918938533204673/1000000000000000 x))
(+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))
(+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))
(pow x 2)
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))
(* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))
(* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* y (- x 1/2))
(* -1/2 y)
(+ (* -1/2 y) (* x y))
(+ (* -1/2 y) (* x y))
(+ (* -1/2 y) (* x y))
(* x y)
(* x (+ y (* -1/2 (/ y x))))
(* x (+ y (* -1/2 (/ y x))))
(* x (+ y (* -1/2 (/ y x))))
(* x y)
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
-1/2
(- x 1/2)
(- x 1/2)
(- x 1/2)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (- 1 (* 1/2 (/ 1 x))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000
(+ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* -1 (pow x 3)))
(+ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* -1 (pow x 3)))
(+ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* -1 (pow x 3)))
(* -1 (pow x 3))
(* (pow x 3) (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))) 1))
(* (pow x 3) (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))) 1))
(* (pow x 3) (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))) 1))
(* -1 (pow x 3))
(* -1 (* (pow x 3) (- 1 (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))))))
(* -1 (* (pow x 3) (- 1 (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))))))
(* -1 (* (pow x 3) (- 1 (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
(- 918938533204673/1000000000000000 x)
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(- (+ 918938533204673/1000000000000000 (* y (- x 1/2))) x)
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* y (- x 1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* y (- (+ x (* 918938533204673/1000000000000000 (/ 1 y))) (+ 1/2 (/ x y))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* y (- x 1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* -1 (* y (+ (* -1 (- x 1/2)) (* -1 (/ (- 918938533204673/1000000000000000 x) y)))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(+ 918938533204673/1000000000000000 (* -1/2 y))
(+.f64 #s(literal 918938533204673/1000000000000000 binary64) (*.f64 y #s(literal -1/2 binary64)))
(+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* x (- y 1))
(*.f64 x (+.f64 y #s(literal -1 binary64)))
(* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* x (- (+ y (+ (* -1/2 (/ y x)) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* -1 (* x (+ 1 (* -1 y))))
(*.f64 x (+.f64 y #s(literal -1 binary64)))
(* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(* -1 (* x (+ 1 (+ (* -1 y) (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/2 y)) x))))))
(+.f64 (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x) (*.f64 y (+.f64 x #s(literal -1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (-.f64 x #s(literal -1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (-.f64 x #s(literal -1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (-.f64 x #s(literal -1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (-.f64 x #s(literal -1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (-.f64 x #s(literal -1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (-.f64 x #s(literal -1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (-.f64 x #s(literal -1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (-.f64 x #s(literal -1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (-.f64 x #s(literal -1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (-.f64 x #s(literal -1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (-.f64 x #s(literal -1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (-.f64 x #s(literal -1/2 binary64))))
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(+ (* -4 (/ x y)) (* 2 (/ 1 y)))
(.f64 (/.f64 #s(literal 1 binary64) y) (+.f64 #s(literal 2 binary64) (.f64 x #s(literal -4 binary64))))
(+ (* x (- (* 8 (/ x y)) (* 4 (/ 1 y)))) (* 2 (/ 1 y)))
(+.f64 (/.f64 #s(literal 2 binary64) y) (.f64 (/.f64 x y) (+.f64 #s(literal -4 binary64) (.f64 x #s(literal 8 binary64)))))
(+ (* x (- (* x (+ (* -16 (/ x y)) (* 8 (/ 1 y)))) (* 4 (/ 1 y)))) (* 2 (/ 1 y)))
(+.f64 (/.f64 #s(literal 2 binary64) y) (.f64 x (+.f64 (.f64 (/.f64 x y) (+.f64 #s(literal 8 binary64) (*.f64 x #s(literal -16 binary64)))) (/.f64 #s(literal -4 binary64) y))))
(/ 1 (* x y))
(/.f64 #s(literal 1 binary64) (*.f64 x y))
(/ (- (/ 1 y) (* 1/2 (/ 1 (* x y)))) x)
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) y) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x))) x)
(/ (- (+ (/ 1/4 (* (pow x 2) y)) (/ 1 y)) (/ 1/2 (* x y))) x)
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) y) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) x))) x)) x)
(/ (- (+ (/ 1 y) (* 1/4 (/ 1 (* (pow x 2) y)))) (+ (/ 1/2 (* x y)) (* 1/8 (/ 1 (* (pow x 3) y))))) x)
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (+.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) y) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) x))) x) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x (.f64 x y)))))) x)
(/ 1 (* x y))
(/.f64 #s(literal 1 binary64) (*.f64 x y))
(* -1 (/ (- (* 1/2 (/ 1 (* x y))) (/ 1 y)) x))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) y) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x))) x)
(* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 (* x y))) (* 1/2 (/ 1 y))) x)) (/ 1 y)) x))
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) y) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) x))) x)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* x y))) (* 1/4 (/ 1 y))) x)) (* 1/2 (/ 1 y))) x)) (/ 1 y)) x))
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 (+.f64 (.f64 (/.f64 #s(literal -1 binary64) (.f64 x y)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/4 binary64))) (/.f64 #s(literal -1/2 binary64) y)) x)) x)
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y (*.f64 y (-.f64 x #s(literal -1/2 binary64)))))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y (*.f64 y (-.f64 x #s(literal -1/2 binary64)))))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y (*.f64 y (-.f64 x #s(literal -1/2 binary64)))))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y (*.f64 y (-.f64 x #s(literal -1/2 binary64)))))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y (*.f64 y (-.f64 x #s(literal -1/2 binary64)))))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y (*.f64 y (-.f64 x #s(literal -1/2 binary64)))))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y (*.f64 y (-.f64 x #s(literal -1/2 binary64)))))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y (*.f64 y (-.f64 x #s(literal -1/2 binary64)))))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y (*.f64 y (-.f64 x #s(literal -1/2 binary64)))))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y (*.f64 y (-.f64 x #s(literal -1/2 binary64)))))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y (*.f64 y (-.f64 x #s(literal -1/2 binary64)))))
(* (pow y 2) (* (+ 1/2 x) (- x 1/2)))
(.f64 (+.f64 x #s(literal -1/2 binary64)) (.f64 y (*.f64 y (-.f64 x #s(literal -1/2 binary64)))))
(* -1/4 (pow y 2))
(.f64 (.f64 y y) #s(literal -1/4 binary64))
(+ (* -1/4 (pow y 2)) (* (pow x 2) (pow y 2)))
(.f64 (.f64 y y) (+.f64 (*.f64 x x) #s(literal -1/4 binary64)))
(+ (* -1/4 (pow y 2)) (* (pow x 2) (pow y 2)))
(.f64 (.f64 y y) (+.f64 (*.f64 x x) #s(literal -1/4 binary64)))
(+ (* -1/4 (pow y 2)) (* (pow x 2) (pow y 2)))
(.f64 (.f64 y y) (+.f64 (*.f64 x x) #s(literal -1/4 binary64)))
(* (pow x 2) (pow y 2))
(.f64 (.f64 x y) (*.f64 x y))
(* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))
(.f64 (.f64 y y) (+.f64 (*.f64 x x) #s(literal -1/4 binary64)))
(* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))
(.f64 (.f64 y y) (+.f64 (*.f64 x x) #s(literal -1/4 binary64)))
(* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))
(.f64 (.f64 y y) (+.f64 (*.f64 x x) #s(literal -1/4 binary64)))
(* (pow x 2) (pow y 2))
(.f64 (.f64 x y) (*.f64 x y))
(* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))
(.f64 (.f64 y y) (+.f64 (*.f64 x x) #s(literal -1/4 binary64)))
(* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))
(.f64 (.f64 y y) (+.f64 (*.f64 x x) #s(literal -1/4 binary64)))
(* (pow x 2) (+ (* -1/4 (/ (pow y 2) (pow x 2))) (pow y 2)))
(.f64 (.f64 y y) (+.f64 (*.f64 x x) #s(literal -1/4 binary64)))
(* y (+ 1/2 x))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(+ (* 1/2 y) (* x y))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(+ (* 1/2 y) (* x y))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(+ (* 1/2 y) (* x y))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* x y)
(*.f64 x y)
(* x (+ y (* 1/2 (/ y x))))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* x (+ y (* 1/2 (/ y x))))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* x (+ y (* 1/2 (/ y x))))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* x y)
(*.f64 x y)
(* -1 (* x (+ (* -1 y) (* -1/2 (/ y x)))))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* -1 (* x (+ (* -1 y) (* -1/2 (/ y x)))))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* -1 (* x (+ (* -1 y) (* -1/2 (/ y x)))))
(*.f64 y (-.f64 x #s(literal -1/2 binary64)))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
918938533204673/1000000000000000
#s(literal 918938533204673/1000000000000000 binary64)
(+ 918938533204673/1000000000000000 (* -1 x))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(+ 918938533204673/1000000000000000 (* -1 x))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(+ 918938533204673/1000000000000000 (* -1 x))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(* 918938533204673/1000000000000000 x)
(*.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* x (+ 918938533204673/1000000000000000 x))
(*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* x (+ 918938533204673/1000000000000000 x))
(*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* x (+ 918938533204673/1000000000000000 x))
(*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
844448027808355901771309036929/1000000000000000000000000000000
#s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64)
(+ 844448027808355901771309036929/1000000000000000000000000000000 (* 918938533204673/1000000000000000 x))
(+.f64 (*.f64 #s(literal 918938533204673/1000000000000000 binary64) x) #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64))
(+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))
(+.f64 (*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x)) #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64))
(+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))
(+.f64 (*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x)) #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))
(.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x x))) x)))
(* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))
(.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x x))) x)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))
(.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x x))) x)))
(* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))
(.f64 x (+.f64 #s(literal 918938533204673/1000000000000000 binary64) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x x))) x)))
(* y (- x 1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* y (- x 1/2))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(+ (* -1/2 y) (* x y))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(+ (* -1/2 y) (* x y))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(+ (* -1/2 y) (* x y))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* x y)
(*.f64 x y)
(* x (+ y (* -1/2 (/ y x))))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* x (+ y (* -1/2 (/ y x))))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* x (+ y (* -1/2 (/ y x))))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* x y)
(*.f64 x y)
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
(* -1 (* x (+ (* -1 y) (* 1/2 (/ y x)))))
(*.f64 y (+.f64 x #s(literal -1/2 binary64)))
-1/2
#s(literal -1/2 binary64)
(- x 1/2)
(+.f64 x #s(literal -1/2 binary64))
(- x 1/2)
(+.f64 x #s(literal -1/2 binary64))
(- x 1/2)
(+.f64 x #s(literal -1/2 binary64))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/2 binary64))
775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000
#s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64)
(+ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* -1 (pow x 3)))
(-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))
(+ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* -1 (pow x 3)))
(-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))
(+ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* -1 (pow x 3)))
(-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))
(* -1 (pow x 3))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(* (pow x 3) (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))) 1))
(-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))
(* (pow x 3) (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))) 1))
(-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))
(* (pow x 3) (- (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))) 1))
(-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))
(* -1 (pow x 3))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(* -1 (* (pow x 3) (- 1 (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))))))
(-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))
(* -1 (* (pow x 3) (- 1 (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))))))
(-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))
(* -1 (* (pow x 3) (- 1 (* 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 1 (pow x 3))))))
(-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval443.0ms (4.1%)

Compiler: Compiled 43305 to 26162 computations (39.6% saved)

prune164.0ms (1.5%)

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	1064	2	1066
Fresh	0	0	0
Picked	2	3	5
Done	0	4	4
Total	1066	9	1075

Accuracy

100.0%

Counts

1075 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	67.2%	(fma.f64 (.f64 (.f64 y y) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
▶	29.0%	(/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))
✓	54.3%	(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
✓	51.4%	(+.f64 (*.f64 y #s(literal -1/2 binary64)) #s(literal 918938533204673/1000000000000000 binary64))
✓	47.3%	(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
✓	25.2%	(*.f64 y x)
✓	24.1%	(*.f64 y #s(literal -1/2 binary64))
✓	49.7%	(*.f64 x (+.f64 y #s(literal -1 binary64)))
✓	29.0%	#s(literal 918938533204673/1000000000000000 binary64)

Compiler

Compiled 68 to 52 computations (23.5% saved)

localize544.0ms (5.1%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	0	(*.f64 y y)
✓	cost-diff	0	(.f64 (.f64 y y) #s(literal -1/4 binary64))
✓	cost-diff	6656	(fma.f64 (.f64 (.f64 y y) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
✓	cost-diff	0	(+.f64 x #s(literal 918938533204673/1000000000000000 binary64))
✓	cost-diff	0	(*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))
✓	cost-diff	0	(/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))
✓	accuracy	100.0%	(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
✓	accuracy	100.0%	(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
✓	accuracy	78.8%	(fma.f64 (.f64 (.f64 y y) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
✓	accuracy	100.0%	(+.f64 x #s(literal 918938533204673/1000000000000000 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))
✓	accuracy	100.0%	(*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))
✓	accuracy	98.6%	(/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))

Rules

3148×	`-lowering-.f32`
3148×	`-lowering-.f64`
2786×	`accelerator-lowering-fma.f32`
2786×	`accelerator-lowering-fma.f64`
1930×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	75
1	53	73
2	115	73
3	305	69
4	833	69
5	2214	69
6	4836	69
7	6901	69
0	8075	66

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000))))
775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000
(+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000)))
844448027808355901771309036929/1000000000000000000000000000000
(* x (+ x 918938533204673/1000000000000000))
x
(+ x 918938533204673/1000000000000000)
918938533204673/1000000000000000
(+ (* (* (* y y) -1/4) (/ 1 (* y (+ x 1/2)))) (- 918938533204673/1000000000000000 x))
(* (* y y) -1/4)
(* y y)
y
-1/4
(/ 1 (* y (+ x 1/2)))
1
(* y (+ x 1/2))
(+ x 1/2)
1/2
(- 918938533204673/1000000000000000 x)

Outputs
(/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000))))
(/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))
775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000
#s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64)
(+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000)))
(+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))
844448027808355901771309036929/1000000000000000000000000000000
#s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64)
(* x (+ x 918938533204673/1000000000000000))
(*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))
x
(+ x 918938533204673/1000000000000000)
(+.f64 x #s(literal 918938533204673/1000000000000000 binary64))
918938533204673/1000000000000000
#s(literal 918938533204673/1000000000000000 binary64)
(+ (* (* (* y y) -1/4) (/ 1 (* y (+ x 1/2)))) (- 918938533204673/1000000000000000 x))
(+.f64 #s(literal 918938533204673/1000000000000000 binary64) (-.f64 (/.f64 (*.f64 y #s(literal -1/4 binary64)) (+.f64 x #s(literal 1/2 binary64))) x))
(* (* y y) -1/4)
(.f64 y (.f64 y #s(literal -1/4 binary64)))
(* y y)
(*.f64 y y)
y
-1/4
#s(literal -1/4 binary64)
(/ 1 (* y (+ x 1/2)))
(/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(* y (+ x 1/2))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(+ x 1/2)
(+.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(- 918938533204673/1000000000000000 x)
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)

Results

102.0ms

256×

valid

Compiler

Compiled 79 to 52 computations (34.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 81.0ms

ival-add: 35.0ms (43.1% of total)

ival-mult: 32.0ms (39.5% of total)

ival-div: 5.0ms (6.2% of total)

<compiled-spec>: 3.0ms (3.7% of total)

ival-sub: 3.0ms (3.7% of total)

const: 3.0ms (3.7% of total)

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

series18.0ms (0.2%)

Counts

10 → 156

Calls

Call 1

Inputs
#<alt (/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000))))>
#<alt (* x (+ x 918938533204673/1000000000000000))>
#<alt (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000)))>
#<alt (+ x 918938533204673/1000000000000000)>
#<alt (+ (* (* (* y y) -1/4) (/ 1 (* y (+ x 1/2)))) (- 918938533204673/1000000000000000 x))>
#<alt (/ 1 (* y (+ x 1/2)))>
#<alt (* y (+ x 1/2))>
#<alt (- 918938533204673/1000000000000000 x)>
#<alt (* (* y y) -1/4)>
#<alt (* y y)>

Outputs
#<alt 918938533204673/1000000000000000>
#<alt (+ 918938533204673/1000000000000000 (* -1 x))>
#<alt (+ 918938533204673/1000000000000000 (* x (- (* 1000000000000000000000000000000/844448027808355901771309036929 (pow x 2)) 1)))>
#<alt (+ 918938533204673/1000000000000000 (* x (- (* (pow x 2) (+ 1000000000000000000000000000000/844448027808355901771309036929 (* -1000000000000000000000000000000000000000000000/775995832041789488711238455368417219672369217 x))) 1)))>
#<alt (/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (pow x 2))>
#<alt (/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* 713092471669421822382614706812434602753285766506341485751041/1000000000000000000000000000000000000000000000000000000000000 (/ 1 x))) (pow x 2))>
#<alt (/ (- (+ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow x 3))) (* 713092471669421822382614706812434602753285766506341485751041/1000000000000000000000000000000000000000000000000000000000000 (/ 1 x))) (pow x 2))>
#<alt (/ (- (+ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow x 3))) (+ (* 713092471669421822382614706812434602753285766506341485751041/1000000000000000000000000000000000000000000000000000000000000 (/ 1 x)) (* 553356785875849185813651753046754059684528638095022056452717715645164869810465386529495301884023094104897/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (/ 1 (pow x 4))))) (pow x 2))>
#<alt (/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (pow x 2))>
#<alt (/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* 713092471669421822382614706812434602753285766506341485751041/1000000000000000000000000000000000000000000000000000000000000 (/ 1 x))) (pow x 2))>
#<alt (/ (+ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* -1 (/ (- 713092471669421822382614706812434602753285766506341485751041/1000000000000000000000000000000000000000000000000000000000000 (* 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (/ 1 (pow x 2)))) x))) (pow x 2))>
#<alt (/ (+ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* -1 (/ (- (+ 713092471669421822382614706812434602753285766506341485751041/1000000000000000000000000000000000000000000000000000000000000 (/ 553356785875849185813651753046754059684528638095022056452717715645164869810465386529495301884023094104897/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow x 3))) (* 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (/ 1 (pow x 2)))) x))) (pow x 2))>
#<alt (* 918938533204673/1000000000000000 x)>
#<alt (* x (+ 918938533204673/1000000000000000 x))>
#<alt (* x (+ 918938533204673/1000000000000000 x))>
#<alt (* x (+ 918938533204673/1000000000000000 x))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt 844448027808355901771309036929/1000000000000000000000000000000>
#<alt (+ 844448027808355901771309036929/1000000000000000000000000000000 (* 918938533204673/1000000000000000 x))>
#<alt (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))>
#<alt (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt 918938533204673/1000000000000000>
#<alt (+ 918938533204673/1000000000000000 x)>
#<alt (+ 918938533204673/1000000000000000 x)>
#<alt (+ 918938533204673/1000000000000000 x)>
#<alt x>
#<alt (* x (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* x (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* x (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* x (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (* x (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))>
#<alt (- 918938533204673/1000000000000000 x)>
#<alt (- (+ 918938533204673/1000000000000000 (* -1/4 (/ y (+ 1/2 x)))) x)>
#<alt (- (+ 918938533204673/1000000000000000 (* -1/4 (/ y (+ 1/2 x)))) x)>
#<alt (- (+ 918938533204673/1000000000000000 (* -1/4 (/ y (+ 1/2 x)))) x)>
#<alt (* -1/4 (/ y (+ 1/2 x)))>
#<alt (* y (- (* 918938533204673/1000000000000000 (/ 1 y)) (+ (* 1/4 (/ 1 (+ 1/2 x))) (/ x y))))>
#<alt (* y (- (* 918938533204673/1000000000000000 (/ 1 y)) (+ (* 1/4 (/ 1 (+ 1/2 x))) (/ x y))))>
#<alt (* y (- (* 918938533204673/1000000000000000 (/ 1 y)) (+ (* 1/4 (/ 1 (+ 1/2 x))) (/ x y))))>
#<alt (* -1/4 (/ y (+ 1/2 x)))>
#<alt (* -1 (* y (+ (* -1 (/ (- 918938533204673/1000000000000000 x) y)) (* 1/4 (/ 1 (+ 1/2 x))))))>
#<alt (* -1 (* y (+ (* -1 (/ (- 918938533204673/1000000000000000 x) y)) (* 1/4 (/ 1 (+ 1/2 x))))))>
#<alt (* -1 (* y (+ (* -1 (/ (- 918938533204673/1000000000000000 x) y)) (* 1/4 (/ 1 (+ 1/2 x))))))>
#<alt (+ 918938533204673/1000000000000000 (* -1/2 y))>
#<alt (+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- y 1))))>
#<alt (+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- (+ y (* -2 (* x y))) 1))))>
#<alt (+ 918938533204673/1000000000000000 (+ (* -1/2 y) (* x (- (+ y (* x (+ (* -2 y) (* 4 (* x y))))) 1))))>
#<alt (* -1 x)>
#<alt (* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))>
#<alt (* x (- (+ (* -1/4 (/ y (pow x 2))) (* 918938533204673/1000000000000000 (/ 1 x))) 1))>
#<alt (* x (- (+ (* -1/4 (/ y (pow x 2))) (+ (* 1/8 (/ y (pow x 3))) (* 918938533204673/1000000000000000 (/ 1 x)))) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (+ 918938533204673/1000000000000000 (* -1/4 (/ y x))) x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (+ 918938533204673/1000000000000000 (* -1 (/ (+ (* -1/8 (/ y x)) (* 1/4 y)) x))) x)))))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 1 (* y (+ 1/2 x)))>
#<alt (/ 2 y)>
#<alt (+ (* -4 (/ x y)) (* 2 (/ 1 y)))>
#<alt (+ (* x (- (* 8 (/ x y)) (* 4 (/ 1 y)))) (* 2 (/ 1 y)))>
#<alt (+ (* x (- (* x (+ (* -16 (/ x y)) (* 8 (/ 1 y)))) (* 4 (/ 1 y)))) (* 2 (/ 1 y)))>
#<alt (/ 1 (* x y))>
#<alt (/ (- (/ 1 y) (* 1/2 (/ 1 (* x y)))) x)>
#<alt (/ (- (+ (/ 1/4 (* (pow x 2) y)) (/ 1 y)) (/ 1/2 (* x y))) x)>
#<alt (/ (- (+ (/ 1 y) (* 1/4 (/ 1 (* (pow x 2) y)))) (+ (/ 1/2 (* x y)) (* 1/8 (/ 1 (* (pow x 3) y))))) x)>
#<alt (/ 1 (* x y))>
#<alt (* -1 (/ (- (* 1/2 (/ 1 (* x y))) (/ 1 y)) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 (* x y))) (* 1/2 (/ 1 y))) x)) (/ 1 y)) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* x y))) (* 1/4 (/ 1 y))) x)) (* 1/2 (/ 1 y))) x)) (/ 1 y)) x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* y (+ 1/2 x))>
#<alt (* 1/2 y)>
#<alt (+ (* 1/2 y) (* x y))>
#<alt (+ (* 1/2 y) (* x y))>
#<alt (+ (* 1/2 y) (* x y))>
#<alt (* x y)>
#<alt (* x (+ y (* 1/2 (/ y x))))>
#<alt (* x (+ y (* 1/2 (/ y x))))>
#<alt (* x (+ y (* 1/2 (/ y x))))>
#<alt (* x y)>
#<alt (* -1 (* x (+ (* -1 y) (* -1/2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* -1/2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* -1/2 (/ y x)))))>
#<alt 918938533204673/1000000000000000>
#<alt (+ 918938533204673/1000000000000000 (* -1 x))>
#<alt (+ 918938533204673/1000000000000000 (* -1 x))>
#<alt (+ 918938533204673/1000000000000000 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))>
#<alt (* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))>
#<alt (* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))>
#<alt (* -1/4 (pow y 2))>
#<alt (* -1/4 (pow y 2))>
#<alt (* -1/4 (pow y 2))>
#<alt (* -1/4 (pow y 2))>
#<alt (* -1/4 (pow y 2))>
#<alt (* -1/4 (pow y 2))>
#<alt (* -1/4 (pow y 2))>
#<alt (* -1/4 (pow y 2))>
#<alt (* -1/4 (pow y 2))>
#<alt (* -1/4 (pow y 2))>
#<alt (* -1/4 (pow y 2))>
#<alt (* -1/4 (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)>

Calls

39 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(+ (* (* (* y y) -1/4) (/ 1 (* y (+ x 1/2)))) (- 918938533204673/1000000000000000 x))
0.0ms	x	@	inf	(/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000))))
0.0ms	y	@	inf	(* (* y y) -1/4)
0.0ms	x	@	0	(+ (* (* (* y y) -1/4) (/ 1 (* y (+ x 1/2)))) (- 918938533204673/1000000000000000 x))
0.0ms	x	@	-inf	(/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000))))

rewrite697.0ms (6.5%)

Algorithm

1×	batch-egg-rewrite

Rules

5906×	`accelerator-lowering-fma.f32`
5906×	`accelerator-lowering-fma.f64`
4122×	`/-lowering-/.f32`
4122×	`/-lowering-/.f64`
3836×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	62
1	128	62
2	1029	60
0	8443	57

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 508

Calls

Call 1

Inputs
(/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000))))
(* x (+ x 918938533204673/1000000000000000))
(+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ x 918938533204673/1000000000000000)))
(+ x 918938533204673/1000000000000000)
(+ (* (* (* y y) -1/4) (/ 1 (* y (+ x 1/2)))) (- 918938533204673/1000000000000000 x))
(/ 1 (* y (+ x 1/2)))
(* y (+ x 1/2))
(- 918938533204673/1000000000000000 x)
(* (* y y) -1/4)
(* y y)

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))) #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (-.f64 #s(literal -844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))))
(neg.f64 (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (-.f64 #s(literal -844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (-.f64 #s(literal -844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))) #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64))))
(/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))) #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))) #s(literal -775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64)))
(/.f64 #s(literal -775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (-.f64 #s(literal -844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))
(pow.f64 (/.f64 (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))) #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (-.f64 #s(literal -844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))))
(.f64 #s(literal -775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))))
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(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64))) (+.f64 (.f64 x x) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))
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(/.f64 (-.f64 (.f64 (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))) (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))) (.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))) (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))))) (+.f64 (/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))) (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))))
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(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(*.f64 #s(literal -1 binary64) (-.f64 x #s(literal 918938533204673/1000000000000000 binary64)))
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(.f64 (-.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))))
(.f64 (+.f64 #s(literal -844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 x) #s(literal -918938533204673/1000000000000000 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))) (.f64 (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))))) (+.f64 #s(literal 713092471669421822382614706812434602753285766506341485751041/1000000000000000000000000000000000000000000000000000000000000 binary64) (.f64 (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))) (+.f64 (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))) #s(literal -844448027808355901771309036929/1000000000000000000000000000000 binary64)))))
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(.f64 (/.f64 (-.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x x)) (+.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (-.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x x)) (+.f64 (*.f64 x x) #s(literal -844448027808355901771309036929/1000000000000000000000000000000 binary64))) (-.f64 x #s(literal 918938533204673/1000000000000000 binary64)))
(.f64 y (.f64 y #s(literal -1/4 binary64)))
(.f64 (.f64 y y) #s(literal -1/4 binary64))
(.f64 #s(literal -1/4 binary64) (.f64 y y))
(.f64 (.f64 y (*.f64 y #s(literal -1/4 binary64))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 y (*.f64 y #s(literal -1/4 binary64))))
(.f64 (.f64 y #s(literal -1/4 binary64)) y)
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))
(pow.f64 y #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(*.f64 y y)
(.f64 (.f64 y y) #s(literal 1 binary64))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))

simplify540.0ms (5%)

Algorithm

1×	egg-herbie

Rules

8720×	`accelerator-lowering-fma.f32`
8720×	`accelerator-lowering-fma.f64`
4092×	`-lowering-.f32`
4092×	`-lowering-.f64`
2482×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	228	1065
1	667	1053
2	1724	1025
3	4957	1019
0	8562	973

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

Inputs
918938533204673/1000000000000000
(+ 918938533204673/1000000000000000 (* -1 x))
(+ 918938533204673/1000000000000000 (* x (- (* 1000000000000000000000000000000/844448027808355901771309036929 (pow x 2)) 1)))
(+ 918938533204673/1000000000000000 (* x (- (* (pow x 2) (+ 1000000000000000000000000000000/844448027808355901771309036929 (* -1000000000000000000000000000000000000000000000/775995832041789488711238455368417219672369217 x))) 1)))
(/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (pow x 2))
(/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* 713092471669421822382614706812434602753285766506341485751041/1000000000000000000000000000000000000000000000000000000000000 (/ 1 x))) (pow x 2))
(/ (- (+ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow x 3))) (* 713092471669421822382614706812434602753285766506341485751041/1000000000000000000000000000000000000000000000000000000000000 (/ 1 x))) (pow x 2))
(/ (- (+ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (/ 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow x 3))) (+ (* 713092471669421822382614706812434602753285766506341485751041/1000000000000000000000000000000000000000000000000000000000000 (/ 1 x)) (* 553356785875849185813651753046754059684528638095022056452717715645164869810465386529495301884023094104897/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (/ 1 (pow x 4))))) (pow x 2))
(/ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (pow x 2))
(/ (- 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* 713092471669421822382614706812434602753285766506341485751041/1000000000000000000000000000000000000000000000000000000000000 (/ 1 x))) (pow x 2))
(/ (+ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* -1 (/ (- 713092471669421822382614706812434602753285766506341485751041/1000000000000000000000000000000000000000000000000000000000000 (* 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (/ 1 (pow x 2)))) x))) (pow x 2))
(/ (+ 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (* -1 (/ (- (+ 713092471669421822382614706812434602753285766506341485751041/1000000000000000000000000000000000000000000000000000000000000 (/ 553356785875849185813651753046754059684528638095022056452717715645164869810465386529495301884023094104897/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow x 3))) (* 602169531346229162124410547214766300102947990270042776016856015928398225588775409969193089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (/ 1 (pow x 2)))) x))) (pow x 2))
(* 918938533204673/1000000000000000 x)
(* x (+ 918938533204673/1000000000000000 x))
(* x (+ 918938533204673/1000000000000000 x))
(* x (+ 918938533204673/1000000000000000 x))
(pow x 2)
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(pow x 2)
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
844448027808355901771309036929/1000000000000000000000000000000
(+ 844448027808355901771309036929/1000000000000000000000000000000 (* 918938533204673/1000000000000000 x))
(+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))
(+ 844448027808355901771309036929/1000000000000000000000000000000 (* x (+ 918938533204673/1000000000000000 x)))
(pow x 2)
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))
(* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))
(* (pow x 2) (+ 1 (+ (/ 844448027808355901771309036929/1000000000000000000000000000000 (pow x 2)) (* 918938533204673/1000000000000000 (/ 1 x)))))
918938533204673/1000000000000000
(+ 918938533204673/1000000000000000 x)
(+ 918938533204673/1000000000000000 x)
(+ 918938533204673/1000000000000000 x)
x
(* x (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* x (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* x (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
x
(* x (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* x (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(* x (+ 1 (* 918938533204673/1000000000000000 (/ 1 x))))
(- 918938533204673/1000000000000000 x)
(- (+ 918938533204673/1000000000000000 (* -1/4 (/ y (+ 1/2 x)))) x)
(- (+ 918938533204673/1000000000000000 (* -1/4 (/ y (+ 1/2 x)))) x)
(- (+ 918938533204673/1000000000000000 (* -1/4 (/ y (+ 1/2 x)))) x)
(* -1/4 (/ y (+ 1/2 x)))
(* y (- (* 918938533204673/1000000000000000 (/ 1 y)) (+ (* 1/4 (/ 1 (+ 1/2 x))) (/ x y))))
(* y (- (* 918938533204673/1000000000000000 (/ 1 y)) (+ (* 1/4 (/ 1 (+ 1/2 x))) (/ x y))))
(* y (- (* 918938533204673/1000000000000000 (/ 1 y)) (+ (* 1/4 (/ 1 (+ 1/2 x))) (/ x y))))
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918938533204673/1000000000000000
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(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
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(pow y 2)
(pow y 2)
(pow y 2)

Outputs
918938533204673/1000000000000000
#s(literal 918938533204673/1000000000000000 binary64)
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844448027808355901771309036929/1000000000000000000000000000000
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918938533204673/1000000000000000
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(/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
(/ 1 (* y (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64))))
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(+ (* -4 (/ x y)) (* 2 (/ 1 y)))
(+.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) #s(literal -4 binary64)))
(+ (* x (- (* 8 (/ x y)) (* 4 (/ 1 y)))) (* 2 (/ 1 y)))
(+.f64 (/.f64 #s(literal 2 binary64) y) (.f64 x (.f64 (/.f64 #s(literal 1 binary64) y) (+.f64 #s(literal -4 binary64) (*.f64 x #s(literal 8 binary64))))))
(+ (* x (- (* x (+ (* -16 (/ x y)) (* 8 (/ 1 y)))) (* 4 (/ 1 y)))) (* 2 (/ 1 y)))
(+.f64 (/.f64 #s(literal 2 binary64) y) (.f64 x (+.f64 (.f64 (/.f64 x y) (+.f64 #s(literal 8 binary64) (*.f64 x #s(literal -16 binary64)))) (/.f64 #s(literal -4 binary64) y))))
(/ 1 (* x y))
(/.f64 #s(literal 1 binary64) (*.f64 x y))
(/ (- (/ 1 y) (* 1/2 (/ 1 (* x y)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 (/.f64 #s(literal -1/2 binary64) y) x)) x)
(/ (- (+ (/ 1/4 (* (pow x 2) y)) (/ 1 y)) (/ 1/2 (* x y))) x)
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x y)) (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -1/2 binary64)))) x)
(/ (- (+ (/ 1 y) (* 1/4 (/ 1 (* (pow x 2) y)))) (+ (/ 1/2 (* x y)) (* 1/8 (/ 1 (* (pow x 3) y))))) x)
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x y)) (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -1/2 binary64))) (/.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x y)) (.f64 x x)))) x)
(/ 1 (* x y))
(/.f64 #s(literal 1 binary64) (*.f64 x y))
(* -1 (/ (- (* 1/2 (/ 1 (* x y))) (/ 1 y)) x))
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 (/.f64 #s(literal -1/2 binary64) y) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 (* x y))) (* 1/2 (/ 1 y))) x)) (/ 1 y)) x))
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x y)) (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -1/2 binary64)))) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* x y))) (* 1/4 (/ 1 y))) x)) (* 1/2 (/ 1 y))) x)) (/ 1 y)) x))
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 (+.f64 (.f64 (/.f64 #s(literal -1 binary64) (.f64 x y)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/4 binary64))) (/.f64 #s(literal -1/2 binary64) y)) x)) x)
(* y (+ 1/2 x))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* y (+ 1/2 x))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* 1/2 y)
(*.f64 y #s(literal 1/2 binary64))
(+ (* 1/2 y) (* x y))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(+ (* 1/2 y) (* x y))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(+ (* 1/2 y) (* x y))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* x y)
(*.f64 x y)
(* x (+ y (* 1/2 (/ y x))))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* x (+ y (* 1/2 (/ y x))))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* x (+ y (* 1/2 (/ y x))))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* x y)
(*.f64 x y)
(* -1 (* x (+ (* -1 y) (* -1/2 (/ y x)))))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* -1 (* x (+ (* -1 y) (* -1/2 (/ y x)))))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
(* -1 (* x (+ (* -1 y) (* -1/2 (/ y x)))))
(*.f64 y (+.f64 x #s(literal 1/2 binary64)))
918938533204673/1000000000000000
#s(literal 918938533204673/1000000000000000 binary64)
(+ 918938533204673/1000000000000000 (* -1 x))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(+ 918938533204673/1000000000000000 (* -1 x))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(+ 918938533204673/1000000000000000 (* -1 x))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* -1 x)
(neg.f64 x)
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* x (- (* 918938533204673/1000000000000000 (/ 1 x)) 1))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* -1 (* x (- 1 (* 918938533204673/1000000000000000 (/ 1 x)))))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(* -1/4 (pow y 2))
(.f64 #s(literal -1/4 binary64) (.f64 y y))
(* -1/4 (pow y 2))
(.f64 #s(literal -1/4 binary64) (.f64 y y))
(* -1/4 (pow y 2))
(.f64 #s(literal -1/4 binary64) (.f64 y y))
(* -1/4 (pow y 2))
(.f64 #s(literal -1/4 binary64) (.f64 y y))
(* -1/4 (pow y 2))
(.f64 #s(literal -1/4 binary64) (.f64 y y))
(* -1/4 (pow y 2))
(.f64 #s(literal -1/4 binary64) (.f64 y y))
(* -1/4 (pow y 2))
(.f64 #s(literal -1/4 binary64) (.f64 y y))
(* -1/4 (pow y 2))
(.f64 #s(literal -1/4 binary64) (.f64 y y))
(* -1/4 (pow y 2))
(.f64 #s(literal -1/4 binary64) (.f64 y y))
(* -1/4 (pow y 2))
(.f64 #s(literal -1/4 binary64) (.f64 y y))
(* -1/4 (pow y 2))
(.f64 #s(literal -1/4 binary64) (.f64 y y))
(* -1/4 (pow y 2))
(.f64 #s(literal -1/4 binary64) (.f64 y y))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)

eval288.0ms (2.7%)

Compiler: Compiled 17408 to 11661 computations (33% saved)

prune156.0ms (1.5%)

Pruning

10 alts after pruning (3 fresh and 7 done)

	Pruned	Kept	Total
New	661	3	664
Fresh	0	0	0
Picked	2	0	2
Done	0	7	7
Total	663	10	673

Accuracy

100.0%

Counts

673 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	70.2%	(fma.f64 (.f64 (.f64 y y) #s(literal -1/4 binary64)) (/.f64 #s(literal 2 binary64) y) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
	28.9%	(/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 (*.f64 #s(literal 918938533204673/1000000000000000 binary64) x) #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64)))
✓	54.3%	(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
✓	51.4%	(+.f64 (*.f64 y #s(literal -1/2 binary64)) #s(literal 918938533204673/1000000000000000 binary64))
✓	47.3%	(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
✓	25.2%	(*.f64 y x)
✓	24.1%	(*.f64 y #s(literal -1/2 binary64))
✓	49.7%	(*.f64 x (+.f64 y #s(literal -1 binary64)))
	26.9%	(neg.f64 x)
✓	29.0%	#s(literal 918938533204673/1000000000000000 binary64)

Compiler

Compiled 217 to 152 computations (30% saved)

regimes23.0ms (0.2%)

Counts

17 → 1

Calls

Call 1

Inputs
#s(literal 918938533204673/1000000000000000 binary64)
(neg.f64 x)
(*.f64 y #s(literal -1/2 binary64))
(*.f64 y x)
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(*.f64 x (+.f64 y #s(literal -1 binary64)))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(+.f64 (*.f64 y #s(literal -1/2 binary64)) #s(literal 918938533204673/1000000000000000 binary64))
(/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 (*.f64 #s(literal 918938533204673/1000000000000000 binary64) x) #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64)))
(+.f64 (*.f64 y (+.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))
(+.f64 (-.f64 (.f64 x (-.f64 y #s(literal 1 binary64))) (.f64 y #s(literal 1/2 binary64))) #s(literal 918938533204673/1000000000000000 binary64))
(/.f64 (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (*.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64)))))
(+.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (/.f64 (-.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64) (.f64 x (+.f64 x #s(literal 918938533204673/1000000000000000 binary64))))))
(fma.f64 (.f64 (.f64 y y) #s(literal -1/4 binary64)) (/.f64 #s(literal 2 binary64) y) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 (.f64 (.f64 y y) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))
(fma.f64 (.f64 (.f64 y (+.f64 x #s(literal -1/2 binary64))) (.f64 y (+.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 y (+.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))

Outputs
(+.f64 (*.f64 y (+.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 918938533204673/1000000000000000 binary64) x))

Calls

4 calls:

6.0ms	y
6.0ms	(-.f64 (.f64 x (-.f64 y #s(literal 1 binary64))) (.f64 y #s(literal 1/2 binary64)))
5.0ms	x
4.0ms	(+.f64 (-.f64 (.f64 x (-.f64 y #s(literal 1 binary64))) (.f64 y #s(literal 1/2 binary64))) #s(literal 918938533204673/1000000000000000 binary64))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(+.f64 (-.f64 (.f64 x (-.f64 y #s(literal 1 binary64))) (.f64 y #s(literal 1/2 binary64))) #s(literal 918938533204673/1000000000000000 binary64))`
100.0%	1	`(-.f64 (.f64 x (-.f64 y #s(literal 1 binary64))) (.f64 y #s(literal 1/2 binary64)))`

Compiler

Compiled 30 to 22 computations (26.7% saved)

regimes21.0ms (0.2%)

Counts

9 → 3

Calls

Call 1

Inputs
#s(literal 918938533204673/1000000000000000 binary64)
(neg.f64 x)
(*.f64 y #s(literal -1/2 binary64))
(*.f64 y x)
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(*.f64 x (+.f64 y #s(literal -1 binary64)))
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(+.f64 (*.f64 y #s(literal -1/2 binary64)) #s(literal 918938533204673/1000000000000000 binary64))
(/.f64 #s(literal 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 binary64) (+.f64 (*.f64 #s(literal 918938533204673/1000000000000000 binary64) x) #s(literal 844448027808355901771309036929/1000000000000000000000000000000 binary64)))

Outputs
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(*.f64 y (-.f64 x #s(literal 1/2 binary64)))

Calls

2 calls:

11.0ms	x
10.0ms	y

Results

Accuracy	Segments	Branch
97.8%	3	`x`
98.1%	3	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes21.0ms (0.2%)

Counts

6 → 5

Calls

Call 1

Inputs
#s(literal 918938533204673/1000000000000000 binary64)
(neg.f64 x)
(*.f64 y #s(literal -1/2 binary64))
(*.f64 y x)
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(*.f64 x (+.f64 y #s(literal -1 binary64)))

Outputs
(*.f64 y #s(literal -1/2 binary64))
(*.f64 y x)
(*.f64 y #s(literal -1/2 binary64))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(*.f64 x (+.f64 y #s(literal -1 binary64)))

Calls

2 calls:

11.0ms	y
10.0ms	x

Results

Accuracy	Segments	Branch
82.2%	7	`x`
81.5%	5	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes9.0ms (0.1%)

Counts

5 → 5

Calls

Call 1

Inputs
#s(literal 918938533204673/1000000000000000 binary64)
(neg.f64 x)
(*.f64 y #s(literal -1/2 binary64))
(*.f64 y x)
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)

Outputs
(*.f64 y #s(literal -1/2 binary64))
(*.f64 y x)
(*.f64 y #s(literal -1/2 binary64))
(-.f64 #s(literal 918938533204673/1000000000000000 binary64) x)
(*.f64 y x)

Calls

1 calls:

9.0ms

Results

Accuracy	Segments	Branch
81.2%	5	`y`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes21.0ms (0.2%)

Counts

4 → 8

Calls

Call 1

Inputs
#s(literal 918938533204673/1000000000000000 binary64)
(neg.f64 x)
(*.f64 y #s(literal -1/2 binary64))
(*.f64 y x)

Outputs
(neg.f64 x)
(*.f64 y x)
#s(literal 918938533204673/1000000000000000 binary64)
(*.f64 y #s(literal -1/2 binary64))
#s(literal 918938533204673/1000000000000000 binary64)
(*.f64 y #s(literal -1/2 binary64))
#s(literal 918938533204673/1000000000000000 binary64)
(neg.f64 x)

Calls

2 calls:

11.0ms	y
9.0ms	x

Results

Accuracy	Segments	Branch
61.5%	8	`x`
62.6%	9	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes14.0ms (0.1%)

Counts

3 → 7

Calls

Call 1

Inputs
#s(literal 918938533204673/1000000000000000 binary64)
(neg.f64 x)
(*.f64 y #s(literal -1/2 binary64))

Outputs
(neg.f64 x)
#s(literal 918938533204673/1000000000000000 binary64)
(*.f64 y #s(literal -1/2 binary64))
#s(literal 918938533204673/1000000000000000 binary64)
(*.f64 y #s(literal -1/2 binary64))
#s(literal 918938533204673/1000000000000000 binary64)
(neg.f64 x)

Calls

2 calls:

7.0ms	y
7.0ms	x

Results

Accuracy	Segments	Branch
56.4%	7	`y`
58.7%	7	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Counts

2 → 3

Calls

Call 1

Inputs
#s(literal 918938533204673/1000000000000000 binary64)
(neg.f64 x)

Outputs
(neg.f64 x)
#s(literal 918938533204673/1000000000000000 binary64)
(neg.f64 x)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
53.1%	3	`x`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes1.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 918938533204673/1000000000000000 binary64)

Outputs
#s(literal 918938533204673/1000000000000000 binary64)

Calls

2 calls:

0.0ms	x
0.0ms	y

Results

Accuracy	Segments	Branch
29.0%	1	`y`
29.0%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch32.0ms (0.3%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	0.0009139651636407531	1.8864209000249639
17.0ms	-7953.751611068106	-1.0208770345348737e-9

Results

16.0ms

288×

valid

Compiler

Compiled 270 to 212 computations (21.5% saved)

Precisions

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

ival-mult: 4.0ms (46% of total)

ival-sub: 3.0ms (34.5% of total)

ival-add: 1.0ms (11.5% of total)

const: 1.0ms (11.5% of total)

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

bsearch107.0ms (1%)

Algorithm

4×	binary-search

Stop Event

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

Steps

Time	Left	Right
13.0ms	6.288312599431621e-26	4.063488910772451e-18
11.0ms	-1357976.1363440345	-7953.751611068106
13.0ms	-2.1197753795439104e+195	-1.9998957381310937e+192
10.0ms	-1.2423984546999864e+290	-2.6566810350973814e+288

Results

30.0ms

496×

valid

Compiler

Compiled 408 to 318 computations (22.1% saved)

Precisions

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

ival-mult: 7.0ms (42.3% of total)

ival-sub: 5.0ms (30.2% of total)

ival-add: 4.0ms (24.2% of total)

const: 1.0ms (6% of total)

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

bsearch55.0ms (0.5%)

Algorithm

4×	binary-search

Stop Event

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

Steps

Time	Left	Right
12.0ms	0.0009139651636407531	1.8864209000249639
10.0ms	-1357976.1363440345	-7953.751611068106
12.0ms	-2.1197753795439104e+195	-1.9998957381310937e+192
16.0ms	-1.2423984546999864e+290	-2.6566810350973814e+288

Results

35.0ms

480×

valid

Compiler

Compiled 378 to 291 computations (23% saved)

Precisions

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

ival-sub: 11.0ms (54.2% of total)

ival-mult: 6.0ms (29.5% of total)

ival-add: 2.0ms (9.8% of total)

const: 1.0ms (4.9% of total)

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

bsearch108.0ms (1%)

Algorithm

7×	binary-search

Stop Event

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

Steps

Time	Left	Right
16.0ms	6.47896934414473e-11	97.92685476088408
12.0ms	2.2629142593259365e-36	9.773677482306133e-33
13.0ms	5.508452928879262e-122	3.399671968283409e-118
13.0ms	-8.956355821414654e-299	-1.2974904303835274e-301
15.0ms	-1.7558612774253526e-97	-3.5074528618960137e-109
11.0ms	-1589.3057279608686	-0.613081725488226
18.0ms	-2.983784335280052e+184	-7.480237297772152e+181

Results

65.0ms

960×

valid

Compiler

Compiled 616 to 528 computations (14.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-mult: 13.0ms (43% of total)

ival-sub: 10.0ms (33.1% of total)

ival-add: 4.0ms (13.2% of total)

const: 2.0ms (6.6% of total)

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

bsearch93.0ms (0.9%)

Algorithm

6×	binary-search

Stop Event

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

Steps

Time	Left	Right
16.0ms	6.47896934414473e-11	97.92685476088408
15.0ms	2.2629142593259365e-36	9.773677482306133e-33
12.0ms	5.508452928879262e-122	3.399671968283409e-118
13.0ms	-8.956355821414654e-299	-1.2974904303835274e-301
15.0ms	-1.7558612774253526e-97	-3.5074528618960137e-109
15.0ms	-659318036186.2128	-1589.3057279608686

Results

56.0ms

848×

valid

Compiler

Compiled 529 to 472 computations (10.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-sub: 14.0ms (42.4% of total)

ival-mult: 12.0ms (36.4% of total)

ival-add: 5.0ms (15.2% of total)

const: 2.0ms (6.1% of total)

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

bsearch45.0ms (0.4%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
27.0ms	6.47896934414473e-11	97.92685476088408
15.0ms	-659318036186.2128	-1589.3057279608686

Results

31.0ms

304×

valid

Compiler

Compiled 189 to 166 computations (12.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 4.0ms (41.4% of total)

ival-sub: 3.0ms (31.1% of total)

ival-add: 1.0ms (10.4% of total)

const: 1.0ms (10.4% of total)

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

soundness2.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 191 to 124 computations (35.1% saved)

preprocess174.0ms (1.6%)

Compiler: Compiled 408 to 268 computations (34.3% saved)

analyze0.0ms (0%)

sample872.0ms (8.1%)

preprocess216.0ms (2%)

explain119.0ms (1.1%)

eval0.0ms (0%)

prune1.0ms (0%)

localize130.0ms (1.2%)

series7.0ms (0.1%)

rewrite615.0ms (5.7%)

simplify422.0ms (3.9%)

eval155.0ms (1.4%)

prune58.0ms (0.5%)

localize449.0ms (4.2%)

series28.0ms (0.3%)

rewrite726.0ms (6.8%)

simplify872.0ms (8.2%)

eval428.0ms (4%)

prune160.0ms (1.5%)

localize523.0ms (4.9%)

series33.0ms (0.3%)

rewrite656.0ms (6.1%)

simplify642.0ms (6%)

eval443.0ms (4.1%)

prune164.0ms (1.5%)

localize544.0ms (5.1%)

series18.0ms (0.2%)

rewrite697.0ms (6.5%)

simplify540.0ms (5%)

eval288.0ms (2.7%)

prune156.0ms (1.5%)

regimes23.0ms (0.2%)

regimes21.0ms (0.2%)

regimes21.0ms (0.2%)

regimes9.0ms (0.1%)

regimes21.0ms (0.2%)

regimes14.0ms (0.1%)

regimes3.0ms (0%)

regimes1.0ms (0%)

bsearch32.0ms (0.3%)

bsearch107.0ms (1%)

bsearch55.0ms (0.5%)

bsearch108.0ms (1%)

bsearch93.0ms (0.9%)

bsearch45.0ms (0.4%)

soundness2.0ms (0%)

preprocess174.0ms (1.6%)

end0.0ms (0%)

Profiling