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

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 8 to 6 computations (25% saved)

Precisions

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

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

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

const: 0.0ms (0% of total)

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

sample594.0ms (32.5%)

Results

411.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 152.0ms

ival-div: 75.0ms (49.5% of total)

ival-sub: 63.0ms (41.6% of total)

const: 11.0ms (7.3% of total)

backward-pass: 3.0ms (2% of total)

Bogosity

preprocess52.0ms (2.8%)

Algorithm

2×	egg-herbie

Rules

300×	`fnmsub-define`
298×	`fmsub-define`
290×	`fnmadd-define`
244×	`fmm-def`
196×	`fnmadd-define`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	34
1	33	32
2	80	30
3	181	24
4	493	24
5	894	24
6	1100	24
7	1112	24
0	5	5
1	7	5
2	17	5
3	26	5
4	40	5
5	76	4
6	146	4
7	246	4
8	344	4
9	519	4
10	654	4
11	713	4
12	721	4
0	721	4

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- x (/ y 4))

Outputs
(- x (/ y 4))
(-.f64 x (/.f64 y #s(literal 4 binary64)))

Call 2

Inputs
(- x (/ y 4))
(- (neg x) (/ y 4))
(- x (/ (neg y) 4))
(neg (- (neg x) (/ y 4)))
(neg (- x (/ (neg y) 4)))
(- y (/ x 4))

Outputs
(- x (/ y 4))
(fma y -1/4 x)
(- (neg x) (/ y 4))
(fnmsub y 1/4 x)
(- x (/ (neg y) 4))
(fma y 1/4 x)
(neg (- (neg x) (/ y 4)))
(fma y 1/4 x)
(neg (- x (/ (neg y) 4)))
(fnmsub y 1/4 x)
(- y (/ x 4))
(fma x -1/4 y)

explain68.0ms (3.7%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(/.f64 y #s(literal 4 binary64))`
-	-	`#s(literal 4 binary64)`
-	-	`y`
-	-	`(-.f64 x (/.f64 y #s(literal 4 binary64)))`

Results

46.0ms

512×

valid

Compiler

Compiled 35 to 17 computations (51.4% saved)

Precisions

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

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

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

const: 1.0ms (10.3% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 x (/.f64 y #s(literal 4 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify25.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 y #s(literal 4 binary64))
✓	cost-diff	0	(-.f64 x (/.f64 y #s(literal 4 binary64)))

Rules

196×	`fnmadd-define`
150×	`sum3-define`
136×	`fnmsub-define`
136×	`fmsub-define`
128×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	7	11
2	17	11
3	26	11
4	40	11
5	76	10
6	146	10
7	246	10
8	344	10
9	519	10
10	654	10
11	713	10
12	721	10
0	721	10

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- x (/ y 4))
x
(/ y 4)
y
4

Outputs
(- x (/ y 4))
(-.f64 x (/.f64 y #s(literal 4 binary64)))
x
(/ y 4)
(/.f64 y #s(literal 4 binary64))
y
4
#s(literal 4 binary64)

localize25.0ms (1.4%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 y #s(literal 4 binary64))
✓	accuracy	100.0%	(-.f64 x (/.f64 y #s(literal 4 binary64)))

Results

19.0ms

256×

valid

Compiler

Compiled 14 to 6 computations (57.1% saved)

Precisions

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

ival-div: 2.0ms (47.6% of total)

ival-sub: 2.0ms (47.6% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Counts

2 → 36

Calls

Call 1

Inputs
#<alt (- x (/ y 4))>
#<alt (/ y 4)>

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

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	(/ y 4)
0.0ms	y	@	inf	(- x (/ y 4))
0.0ms	y	@	0	(- x (/ y 4))
0.0ms	y	@	inf	(/ y 4)
0.0ms	x	@	inf	(- x (/ y 4))

rewrite257.0ms (14.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3186×	`-lowering-.f32`
3186×	`-lowering-.f64`
1548×	`/-lowering-/.f32`
1548×	`/-lowering-/.f64`
1274×	`unpow-prod-down`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	30	8
2	256	7
3	4310	7
0	8476	7

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 113

Calls

Call 1

Inputs
(- x (/ y 4))
(/ y 4)

Outputs
(+.f64 x (/.f64 y #s(literal -4 binary64)))
(+.f64 (/.f64 y #s(literal -4 binary64)) x)
(+.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))) (neg.f64 (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))))
(+.f64 (/.f64 (.f64 x x) (-.f64 x (/.f64 y #s(literal -4 binary64)))) (neg.f64 (/.f64 (.f64 y (*.f64 y #s(literal 1/16 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal -4 binary64))))) #s(literal -1 binary64)))
(-.f64 x (/.f64 y #s(literal 4 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 (/.f64 y #s(literal 4 binary64)) x))
(-.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))) (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (/.f64 y #s(literal -4 binary64)))) (/.f64 (.f64 y (*.f64 y #s(literal 1/16 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64)))))
(-.f64 (+.f64 x #s(literal 0 binary64)) (/.f64 y #s(literal 4 binary64)))
(fma.f64 x #s(literal 1 binary64) (/.f64 y #s(literal -4 binary64)))
(fma.f64 x (/.f64 x (-.f64 x (/.f64 y #s(literal -4 binary64)))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64))))))
(fma.f64 x (/.f64 (.f64 x x) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))) (neg.f64 (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x x) (/.f64 (*.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))))
(fma.f64 y #s(literal -1/4 binary64) x)
(fma.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 1/4 binary64) x)
(fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))) (neg.f64 (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))))
(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 y #s(literal -4 binary64)))) (neg.f64 (/.f64 (.f64 y (*.f64 y #s(literal 1/16 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64))))))
(fma.f64 (.f64 x x) (/.f64 x (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))) (neg.f64 (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x x) (/.f64 (*.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))))
(fma.f64 #s(literal 1 binary64) x (/.f64 y #s(literal -4 binary64)))
(fma.f64 #s(literal -1 binary64) (/.f64 y #s(literal 4 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))) (neg.f64 (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))))
(fma.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (/.f64 y (/.f64 #s(literal -16 binary64) y)))) (+.f64 x (/.f64 y #s(literal -4 binary64))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64))))))
(fma.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)))) (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 4 binary64)) x) (/.f64 #s(literal 4 binary64) y))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64))))))
(fma.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)) (.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (.f64 (-.f64 x (/.f64 y #s(literal -4 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64)))))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)) (-.f64 (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)) (.f64 x x)))) (neg.f64 (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))))
(fma.f64 (/.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (.f64 (-.f64 x (/.f64 y #s(literal -4 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64))))))) (-.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))) (neg.f64 (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x x) (/.f64 (*.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))))
(neg.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))))
(neg.f64 (/.f64 (+.f64 (*.f64 x x) (/.f64 y (/.f64 #s(literal -16 binary64) y))) (-.f64 #s(literal 0 binary64) (-.f64 x (/.f64 y #s(literal -4 binary64))))))
(neg.f64 (/.f64 (+.f64 (neg.f64 (.f64 x (.f64 x x))) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64))) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))))
(neg.f64 (/.f64 (+.f64 (neg.f64 (.f64 x x)) (.f64 y (*.f64 y #s(literal 1/16 binary64)))) (-.f64 x (/.f64 y #s(literal -4 binary64)))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64))) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64))) (+.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (-.f64 (.f64 x x) (/.f64 (.f64 x y) #s(literal -4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal -4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 1 binary64)))
(/.f64 (+.f64 (*.f64 x x) (/.f64 y (/.f64 #s(literal -16 binary64) y))) (-.f64 x (/.f64 y #s(literal -4 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal -4 binary64))))))
(/.f64 (+.f64 (neg.f64 (.f64 x (.f64 x x))) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))))
(/.f64 (+.f64 (neg.f64 (.f64 x x)) (.f64 y (*.f64 y #s(literal 1/16 binary64)))) (-.f64 #s(literal 0 binary64) (-.f64 x (/.f64 y #s(literal -4 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) #s(literal 262144 binary64))) (.f64 (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))) (+.f64 (.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)))) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) #s(literal 4096 binary64))) (.f64 (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))) (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (*.f64 y y)) #s(literal 64 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) #s(literal 4096 binary64))) (.f64 (-.f64 x (/.f64 y #s(literal -4 binary64))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 1/16 binary64))))))))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 256 binary64))) (.f64 (-.f64 x (/.f64 y #s(literal -4 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 1/16 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))) (.f64 (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)))) (.f64 (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))) (+.f64 (.f64 x x) (/.f64 (*.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x (/.f64 y #s(literal -4 binary64)))) (.f64 (-.f64 x (/.f64 y #s(literal -4 binary64))) (.f64 y (.f64 y #s(literal 1/16 binary64))))) (.f64 (-.f64 x (/.f64 y #s(literal -4 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64)))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) #s(literal 262144 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) #s(literal 4096 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64))) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) #s(literal 4096 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (+.f64 (.f64 x x) (.f64 y (*.f64 y #s(literal 1/16 binary64)))))) (-.f64 x (/.f64 y #s(literal -4 binary64)))))
(/.f64 (.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 256 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x x) (.f64 y (*.f64 y #s(literal 1/16 binary64)))) (-.f64 x (/.f64 y #s(literal -4 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 x x) (/.f64 y (/.f64 #s(literal -16 binary64) y))) #s(literal 1 binary64)) (-.f64 x (/.f64 y #s(literal -4 binary64))))
(/.f64 (.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x x) (/.f64 (*.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))
(/.f64 (neg.f64 (+.f64 (neg.f64 (.f64 x (.f64 x x))) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))))
(/.f64 (neg.f64 (+.f64 (neg.f64 (.f64 x x)) (.f64 y (*.f64 y #s(literal 1/16 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 x (/.f64 y #s(literal -4 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))) (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))) (+.f64 (.f64 (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))) (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))) (.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))) (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x x) (/.f64 (*.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 x x) (-.f64 x (/.f64 y #s(literal -4 binary64)))) (/.f64 (.f64 x x) (-.f64 x (/.f64 y #s(literal -4 binary64))))) (+.f64 (.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64))))) (.f64 (/.f64 (.f64 x x) (-.f64 x (/.f64 y #s(literal -4 binary64)))) (/.f64 (.f64 y (*.f64 y #s(literal 1/16 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64))))))))
(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (*.f64 x x)) (-.f64 (/.f64 y #s(literal -4 binary64)) x))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))) (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))) (.f64 (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))) (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))))) (+.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))) (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (-.f64 x (/.f64 y #s(literal -4 binary64)))) (/.f64 (.f64 x x) (-.f64 x (/.f64 y #s(literal -4 binary64))))) (.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64)))))) (+.f64 (/.f64 (.f64 x x) (-.f64 x (/.f64 y #s(literal -4 binary64)))) (/.f64 (.f64 y (*.f64 y #s(literal 1/16 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) #s(literal 262144 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))) (+.f64 (.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)))) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) #s(literal 4096 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))) (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (*.f64 y y)) #s(literal 64 binary64))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) #s(literal 4096 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 y #s(literal -4 binary64))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 1/16 binary64)))))))
(/.f64 (.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 256 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 y #s(literal -4 binary64))))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 1/16 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 (*.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))))
(.f64 (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))) (.f64 (+.f64 x (/.f64 y #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))))
(.f64 (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))) (/.f64 (+.f64 x (/.f64 y #s(literal -4 binary64))) (+.f64 (.f64 x x) (/.f64 (*.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))))
(*.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal -4 binary64))))
(.f64 (+.f64 (.f64 x x) (/.f64 y (/.f64 #s(literal -16 binary64) y))) (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 y #s(literal -4 binary64)))))
(.f64 (-.f64 x (/.f64 y #s(literal -4 binary64))) (.f64 (+.f64 x (/.f64 y #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 y #s(literal -4 binary64))))))
(*.f64 (-.f64 x (/.f64 y #s(literal -4 binary64))) (/.f64 (+.f64 x (/.f64 y #s(literal -4 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64)))))
(.f64 (+.f64 (neg.f64 (.f64 x (.f64 x x))) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (/.f64 (*.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))))
(.f64 (+.f64 (neg.f64 (.f64 x x)) (.f64 y (.f64 y #s(literal 1/16 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x (/.f64 y #s(literal -4 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))) (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (*.f64 y y)) #s(literal 64 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (*.f64 y y)) #s(literal 64 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 y #s(literal -4 binary64)))) (+.f64 (.f64 x x) (/.f64 y (/.f64 #s(literal -16 binary64) y))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 y #s(literal -4 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 y (/.f64 #s(literal -16 binary64) y)))) #s(literal -1 binary64)))
(.f64 (/.f64 (+.f64 (.f64 x x) (/.f64 y (/.f64 #s(literal -16 binary64) y))) (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 4 binary64)) x) (/.f64 #s(literal 4 binary64) y))))
(.f64 (/.f64 (+.f64 (.f64 x x) (/.f64 y (/.f64 #s(literal -16 binary64) y))) (+.f64 (*.f64 x x) (/.f64 y (/.f64 #s(literal -16 binary64) y)))) (+.f64 x (/.f64 y #s(literal -4 binary64))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)) (.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (.f64 (-.f64 x (/.f64 y #s(literal -4 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64)))))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)) (-.f64 (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64)) (*.f64 x x)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (.f64 (-.f64 x (/.f64 y #s(literal -4 binary64))) (-.f64 x (/.f64 y #s(literal -4 binary64))))))) (-.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))))
(.f64 (pow.f64 (/.f64 (-.f64 x (/.f64 y #s(literal -4 binary64))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) #s(literal 4096 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 1/16 binary64))))))))
(.f64 (pow.f64 (/.f64 (-.f64 x (/.f64 y #s(literal -4 binary64))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 256 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 1/16 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) #s(literal 262144 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)) (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 64 binary64)))) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) (/.f64 (.f64 y (-.f64 x (/.f64 y #s(literal -4 binary64)))) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) #s(literal 4096 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (*.f64 y y)) #s(literal 64 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 4 binary64) y)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 y #s(literal 4 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 y #s(literal -4 binary64)))
(neg.f64 (/.f64 y #s(literal -4 binary64)))
(neg.f64 (*.f64 (/.f64 y #s(literal -4 binary64)) #s(literal 1 binary64)))
(/.f64 y #s(literal 4 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) y) #s(literal -4 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) y))
(/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -4 binary64) y))
(pow.f64 (/.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 4 binary64) y) #s(literal -1 binary64))
(*.f64 y #s(literal 1/4 binary64))
(*.f64 (/.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) y) #s(literal -1/4 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 y #s(literal 4 binary64)))
(*.f64 #s(literal 1/4 binary64) y)
(*.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y)))
(*.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 y #s(literal -4 binary64)))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 y #s(literal -4 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal -1/4 binary64) (-.f64 #s(literal 0 binary64) y))
(*.f64 #s(literal -1/4 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) y)) #s(literal -1 binary64)))
(*.f64 #s(literal -1/4 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y)) #s(literal 1/4 binary64))
(*.f64 (pow.f64 (/.f64 y #s(literal 4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 y #s(literal 4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) y)) #s(literal -1 binary64)) #s(literal -1/4 binary64))
(*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 1 binary64)) #s(literal -1/4 binary64))
(*.f64 (pow.f64 (pow.f64 (/.f64 y #s(literal 4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (/.f64 y #s(literal 4 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))

simplify112.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

2256×	`fnmadd-define`
1614×	`fma-define`
1120×	`-lowering-.f32`
1120×	`-lowering-.f64`
1112×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	138
1	70	120
2	187	120
3	552	120
4	1613	120
5	4131	120
0	8143	120

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
(* -1/4 y)
(- x (* 1/4 y))
(- x (* 1/4 y))
(- x (* 1/4 y))
x
(* x (+ 1 (* -1/4 (/ y x))))
(* x (+ 1 (* -1/4 (/ y x))))
(* x (+ 1 (* -1/4 (/ y x))))
x
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
x
(+ x (* -1/4 y))
(+ x (* -1/4 y))
(+ x (* -1/4 y))
(* -1/4 y)
(* y (- (/ x y) 1/4))
(* y (- (/ x y) 1/4))
(* y (- (/ x y) 1/4))
(* -1/4 y)
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)

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

eval27.0ms (1.5%)

Compiler: Compiled 3435 to 338 computations (90.2% saved)

prune51.0ms (2.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	147	3	150

Accuracy

100.0%

Counts

150 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 x (/.f64 y #s(literal 4 binary64)))
▶	51.8%	(*.f64 #s(literal -1/4 binary64) y)
▶	49.9%	x

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal -1/4 binary64) y)

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	5	6
0	5	6

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
x
(* -1/4 y)
-1/4
y

Outputs
x
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
-1/4
#s(literal -1/4 binary64)
y

localize36.0ms (1.9%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal -1/4 binary64) y)

Results

30.0ms

256×

valid

Compiler

Compiled 9 to 5 computations (44.4% saved)

Precisions

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

ival-mult: 2.0ms (80.2% of total)

const: 0.0ms (0% of total)

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

series0.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (* -1/4 y)>

Outputs
#<alt (* -1/4 y)>
#<alt (* -1/4 y)>
#<alt (* -1/4 y)>
#<alt (* -1/4 y)>
#<alt (* -1/4 y)>
#<alt (* -1/4 y)>
#<alt (* -1/4 y)>
#<alt (* -1/4 y)>
#<alt (* -1/4 y)>
#<alt (* -1/4 y)>
#<alt (* -1/4 y)>
#<alt (* -1/4 y)>

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	y	@	0	(* -1/4 y)
0.0ms	y	@	inf	(* -1/4 y)
0.0ms	y	@	-inf	(* -1/4 y)

rewrite13.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

1 → 2

Calls

Call 1

Inputs
(* -1/4 y)

Outputs
(*.f64 #s(literal -1/4 binary64) y)
(*.f64 y #s(literal -1/4 binary64))

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	36
1	4	36
0	4	36

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

Inputs
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)

Outputs
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)

eval1.0ms (0.1%)

Compiler: Compiled 44 to 5 computations (88.6% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	14	3	17

Accuracy

100.0%

Counts

17 → 3

Alt Table

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Status	Accuracy	Program
✓	100.0%	(-.f64 x (/.f64 y #s(literal 4 binary64)))
✓	51.8%	(*.f64 #s(literal -1/4 binary64) y)
✓	49.9%	x

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes12.0ms (0.6%)

Counts

3 → 1

Calls

Call 1

Inputs
x
(*.f64 #s(literal -1/4 binary64) y)
(-.f64 x (/.f64 y #s(literal 4 binary64)))

Outputs
(-.f64 x (/.f64 y #s(literal 4 binary64)))

Calls

4 calls:

6.0ms	x
2.0ms	(-.f64 x (/.f64 y #s(literal 4 binary64)))
2.0ms	(/.f64 y #s(literal 4 binary64))
2.0ms	y

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(-.f64 x (/.f64 y #s(literal 4 binary64)))`
100.0%	1	`(/.f64 y #s(literal 4 binary64))`

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes3.0ms (0.2%)

Counts

2 → 3

Calls

Call 1

Inputs
x
(*.f64 #s(literal -1/4 binary64) y)

Outputs
x
(*.f64 #s(literal -1/4 binary64) y)
x

Calls

2 calls:

2.0ms	x
2.0ms	y

Results

Accuracy	Segments	Branch
77.1%	3	`x`
77.1%	3	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0.2%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

2 calls:

1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
49.9%	1	`y`
49.9%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch20.0ms (1.1%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
12.0ms	7.737488241708513e+132	2.6942420243029285e+138
6.0ms	-253086696155.17508	-73780302847.89941

Results

11.0ms

224×

valid

Compiler

Compiled 152 to 121 computations (20.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-div: 2.0ms (58% of total)

ival-sub: 1.0ms (29% of total)

const: 0.0ms (0% of total)

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

simplify9.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	19	19
2	28	19
3	34	19
4	39	19
5	41	19

Stop Event

1×

saturated

Calls

Call 1

Inputs

(-.f64 x (/.f64 y #s(literal 4 binary64)))

(if (<=.f64 x #s(literal -170000000000 binary64)) x (if (<=.f64 x #s(literal 7800000000000000023035440609764707306225245270208055445667293615954891386067581332557867136688329716277136586495271403190824982282240 binary64)) (*.f64 #s(literal -1/4 binary64) y) x))

Outputs
(-.f64 x (/.f64 y #s(literal 4 binary64)))
(if (<=.f64 x #s(literal -170000000000 binary64)) x (if (<=.f64 x #s(literal 7800000000000000023035440609764707306225245270208055445667293615954891386067581332557867136688329716277136586495271403190824982282240 binary64)) (*.f64 #s(literal -1/4 binary64) y) x))
(if (<=.f64 x #s(literal -170000000000 binary64)) x (if (<=.f64 x #s(literal 7800000000000000023035440609764707306225245270208055445667293615954891386067581332557867136688329716277136586495271403190824982282240 binary64)) (*.f64 y #s(literal -1/4 binary64)) x))
x

soundness480.0ms (26.3%)

Rules

2256×	`fnmadd-define`
1614×	`fma-define`
1120×	`-lowering-.f32`
1120×	`-lowering-.f64`
1112×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	138
1	70	120
2	187	120
3	552	120
4	1613	120
5	4131	120
0	8143	120

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 32 to 21 computations (34.4% saved)

preprocess26.0ms (1.4%)

Compiler: Compiled 56 to 36 computations (35.7% saved)

Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, E

analyze0.0ms (0%)

sample594.0ms (32.5%)

preprocess52.0ms (2.8%)

explain68.0ms (3.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify25.0ms (1.4%)

localize25.0ms (1.4%)

series2.0ms (0.1%)

rewrite257.0ms (14.1%)

simplify112.0ms (6.1%)

eval27.0ms (1.5%)

prune51.0ms (2.8%)

simplify5.0ms (0.3%)

localize36.0ms (1.9%)

series0.0ms (0%)

rewrite13.0ms (0.7%)

simplify4.0ms (0.2%)

eval1.0ms (0.1%)

prune2.0ms (0.1%)

regimes12.0ms (0.6%)

regimes3.0ms (0.2%)

regimes3.0ms (0.2%)

bsearch20.0ms (1.1%)

simplify9.0ms (0.5%)

soundness480.0ms (26.3%)

preprocess26.0ms (1.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	5	11
1	7	11
2	17	11
3	26	11
4	40	11
5	76	10
6	146	10
7	246	10
8	344	10
9	519	10
10	654	10
11	713	10
12	721	10
0	721	10

Iter	Nodes	Cost
0	5	11
1	7	11
2	17	11
3	26	11
4	40	11
5	76	10
6	146	10
7	246	10
8	344	10
9	519	10
10	654	10
11	713	10
12	721	10
0	721	10

Iter	Nodes	Cost
0	5	11
1	7	11
2	17	11
3	26	11
4	40	11
5	76	10
6	146	10
7	246	10
8	344	10
9	519	10
10	654	10
11	713	10
12	721	10
0	721	10