Metrics for Data.Colour.CIE:cieLAB from colour-2.3.3, C

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-add: 0.0ms (0% of total)

const: 0.0ms (0% of total)

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

sample701.0ms (29.9%)

Results

501.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 228.0ms

ival-div: 122.0ms (53.5% of total)

ival-add: 93.0ms (40.8% of total)

const: 11.0ms (4.8% of total)

backward-pass: 3.0ms (1.3% of total)

Bogosity

preprocess33.0ms (1.4%)

Algorithm

2×	egg-herbie

Rules

292×	`fnmadd-define`
288×	`fnmsub-define`
288×	`fmsub-define`
226×	`fmm-def`
140×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	34
1	34	30
2	79	30
3	235	25
4	556	24
5	882	24
6	1067	24
7	1088	24
0	5	5
1	6	5
0	6	5

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(+ x (/ y 500))

Outputs
(+ x (/ y 500))
(+.f64 x (/.f64 y #s(literal 500 binary64)))

Call 2

Inputs
(+ x (/ y 500))
(+ (neg x) (/ y 500))
(+ x (/ (neg y) 500))
(neg (+ (neg x) (/ y 500)))
(neg (+ x (/ (neg y) 500)))
(+ y (/ x 500))

Outputs
(+ x (/ y 500))
(fma y 1/500 x)
(+ (neg x) (/ y 500))
(fnmsub y -1/500 x)
(+ x (/ (neg y) 500))
(fma y -1/500 x)
(neg (+ (neg x) (/ y 500)))
(fma y -1/500 x)
(neg (+ x (/ (neg y) 500)))
(fnmsub y -1/500 x)
(+ y (/ x 500))
(fma x 1/500 y)

explain47.0ms (2%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(/.f64 y #s(literal 500 binary64))`
-	-	`(+.f64 x (/.f64 y #s(literal 500 binary64)))`
-	-	`#s(literal 500 binary64)`
-	-	`y`

Results

27.0ms

512×

valid

Compiler

Compiled 35 to 17 computations (51.4% saved)

Precisions

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

ival-div: 5.0ms (56.9% of total)

ival-add: 3.0ms (34.1% of total)

const: 1.0ms (11.4% 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 500 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 y #s(literal 500 binary64))
✓	cost-diff	0	(+.f64 x (/.f64 y #s(literal 500 binary64)))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	6	11
0	6	11

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ x (/ y 500))
x
(/ y 500)
y
500

Outputs
(+ x (/ y 500))
(+.f64 x (/.f64 y #s(literal 500 binary64)))
x
(/ y 500)
(/.f64 y #s(literal 500 binary64))
y
500
#s(literal 500 binary64)

localize22.0ms (0.9%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 y #s(literal 500 binary64))
✓	accuracy	100.0%	(+.f64 x (/.f64 y #s(literal 500 binary64)))

Results

15.0ms

256×

valid

Compiler

Compiled 14 to 6 computations (57.1% saved)

Precisions

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

ival-add: 4.0ms (62.1% of total)

ival-div: 2.0ms (31% 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 500))>
#<alt (/ y 500)>

Outputs
#<alt (* 1/500 y)>
#<alt (+ x (* 1/500 y))>
#<alt (+ x (* 1/500 y))>
#<alt (+ x (* 1/500 y))>
#<alt x>
#<alt (* x (+ 1 (* 1/500 (/ y x))))>
#<alt (* x (+ 1 (* 1/500 (/ y x))))>
#<alt (* x (+ 1 (* 1/500 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/500 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1/500 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1/500 (/ y x)) 1)))>
#<alt x>
#<alt (+ x (* 1/500 y))>
#<alt (+ x (* 1/500 y))>
#<alt (+ x (* 1/500 y))>
#<alt (* 1/500 y)>
#<alt (* y (+ 1/500 (/ x y)))>
#<alt (* y (+ 1/500 (/ x y)))>
#<alt (* y (+ 1/500 (/ x y)))>
#<alt (* 1/500 y)>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1/500)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1/500)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1/500)))>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	y	@	-inf	(/ y 500)
0.0ms	y	@	inf	(+ x (/ y 500))
0.0ms	x	@	inf	(+ x (/ y 500))
0.0ms	y	@	inf	(/ y 500)
0.0ms	x	@	0	(+ x (/ y 500))

rewrite286.0ms (12.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3020×	`-lowering-.f32`
3020×	`-lowering-.f64`
1446×	`/-lowering-/.f32`
1446×	`/-lowering-/.f64`
1194×	`unpow-prod-down`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	29	7
2	249	7
3	3987	7
0	8280	7

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 105

Calls

Call 1

Inputs
(+ x (/ y 500))
(/ y 500)

Outputs
(+.f64 x (/.f64 y #s(literal 500 binary64)))
(+.f64 (/.f64 y #s(literal 500 binary64)) x)
(+.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y #s(literal -500 binary64)))) (neg.f64 (/.f64 (.f64 y (*.f64 y #s(literal 1/250000 binary64))) (+.f64 x (/.f64 y #s(literal -500 binary64))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal 500 binary64))))) #s(literal -1 binary64)))
(-.f64 x (/.f64 y #s(literal -500 binary64)))
(-.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y #s(literal -500 binary64)))) (/.f64 (.f64 y (*.f64 y #s(literal 1/250000 binary64))) (+.f64 x (/.f64 y #s(literal -500 binary64)))))
(-.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (-.f64 (/.f64 y #s(literal 500 binary64)) x)) (/.f64 (*.f64 x x) (-.f64 (/.f64 y #s(literal 500 binary64)) x)))
(fma.f64 x #s(literal 1 binary64) (/.f64 y #s(literal 500 binary64)))
(fma.f64 x (/.f64 x (+.f64 x (/.f64 y #s(literal -500 binary64)))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (+.f64 x (/.f64 y #s(literal -500 binary64))))))
(fma.f64 y #s(literal 1/500 binary64) x)
(fma.f64 (-.f64 #s(literal 0 binary64) y) #s(literal -1/500 binary64) x)
(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal -500 binary64)))) (neg.f64 (/.f64 (.f64 y (*.f64 y #s(literal 1/250000 binary64))) (+.f64 x (/.f64 y #s(literal -500 binary64))))))
(fma.f64 #s(literal 1 binary64) x (/.f64 y #s(literal 500 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 y #s(literal 500 binary64)) x)
(fma.f64 #s(literal 1/500 binary64) y x)
(fma.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (/.f64 y (/.f64 #s(literal -250000 binary64) y)))) (+.f64 x (/.f64 y #s(literal 500 binary64))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (+.f64 x (/.f64 y #s(literal -500 binary64))))))
(fma.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/125000000 binary64)))) (+.f64 (.f64 x x) (.f64 (/.f64 y #s(literal 500 binary64)) (+.f64 x (/.f64 y #s(literal 500 binary64))))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (+.f64 x (/.f64 y #s(literal -500 binary64))))))
(neg.f64 (/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/125000000 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y))))))
(neg.f64 (/.f64 (+.f64 (*.f64 x x) (/.f64 y (/.f64 #s(literal -250000 binary64) y))) (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 y #s(literal -500 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/125000000 binary64)))) (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (/.f64 y (/.f64 #s(literal -250000 binary64) y)))) (+.f64 x (/.f64 y #s(literal -500 binary64)))))
(/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/125000000 binary64))) (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal 500 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal 500 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (-.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (*.f64 x x))))
(/.f64 (+.f64 (*.f64 x x) (/.f64 y (/.f64 #s(literal -250000 binary64) y))) (+.f64 x (/.f64 y #s(literal -500 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal 500 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/125000000 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y)))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (/.f64 y (/.f64 #s(literal -250000 binary64) y)))) (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 y #s(literal -500 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 1953125000000000000000000 binary64))) (.f64 (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 125000000 binary64)) (-.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 125000000 binary64)) (.f64 x (.f64 x x)))))))
(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (*.f64 x x)) (-.f64 (/.f64 y #s(literal 500 binary64)) 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 15625000000000000 binary64))) (.f64 (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y))) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (*.f64 y y)) #s(literal -1/125000000 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 15625000000000000 binary64))) (.f64 (+.f64 x (/.f64 y #s(literal -500 binary64))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 1/250000 binary64))))))))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 62500000000 binary64))) (.f64 (+.f64 x (/.f64 y #s(literal -500 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 1/250000 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x (/.f64 y #s(literal -500 binary64)))) (.f64 (+.f64 x (/.f64 y #s(literal -500 binary64))) (.f64 y (.f64 y #s(literal 1/250000 binary64))))) (.f64 (+.f64 x (/.f64 y #s(literal -500 binary64))) (+.f64 x (/.f64 y #s(literal -500 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 1953125000000000000000000 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 125000000 binary64)) (-.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 125000000 binary64)) (.f64 x (.f64 x x))))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y)))))
(/.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 15625000000000000 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/125000000 binary64))) (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y)))))
(/.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 15625000000000000 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (+.f64 (.f64 x x) (.f64 y (*.f64 y #s(literal 1/250000 binary64)))))) (+.f64 x (/.f64 y #s(literal -500 binary64)))))
(/.f64 (.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 62500000000 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x x) (.f64 y (*.f64 y #s(literal 1/250000 binary64)))) (+.f64 x (/.f64 y #s(literal -500 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/125000000 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (/.f64 y (/.f64 #s(literal -250000 binary64) y))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 y #s(literal -500 binary64))))))
(/.f64 (neg.f64 (-.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (*.f64 x x))) (neg.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y #s(literal -500 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (+.f64 x (/.f64 y #s(literal -500 binary64)))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y #s(literal -500 binary64)))) (/.f64 (.f64 x x) (+.f64 x (/.f64 y #s(literal -500 binary64))))) (+.f64 (.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (+.f64 x (/.f64 y #s(literal -500 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (+.f64 x (/.f64 y #s(literal -500 binary64))))) (.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y #s(literal -500 binary64)))) (/.f64 (.f64 y (*.f64 y #s(literal 1/250000 binary64))) (+.f64 x (/.f64 y #s(literal -500 binary64))))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y #s(literal -500 binary64)))) (/.f64 (.f64 x x) (+.f64 x (/.f64 y #s(literal -500 binary64))))) (.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (+.f64 x (/.f64 y #s(literal -500 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (+.f64 x (/.f64 y #s(literal -500 binary64)))))) (+.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y #s(literal -500 binary64)))) (/.f64 (.f64 y (*.f64 y #s(literal 1/250000 binary64))) (+.f64 x (/.f64 y #s(literal -500 binary64))))))
(/.f64 (.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/125000000 binary64))) #s(literal 1 binary64)) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y))))
(/.f64 (.f64 (+.f64 (.f64 x x) (/.f64 y (/.f64 #s(literal -250000 binary64) y))) #s(literal 1 binary64)) (+.f64 x (/.f64 y #s(literal -500 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 1953125000000000000000000 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y))))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 125000000 binary64)) (-.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 125000000 binary64)) (.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 15625000000000000 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y))))) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (*.f64 y y)) #s(literal -1/125000000 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 15625000000000000 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal -500 binary64))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 1/250000 binary64)))))))
(/.f64 (.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 62500000000 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal -500 binary64))))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 1/250000 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal 500 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal 500 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (-.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (*.f64 x x))) #s(literal -1 binary64))
(.f64 (+.f64 x (/.f64 y #s(literal 500 binary64))) (.f64 (+.f64 x (/.f64 y #s(literal -500 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal -500 binary64))))))
(*.f64 (+.f64 x (/.f64 y #s(literal 500 binary64))) (/.f64 (+.f64 x (/.f64 y #s(literal -500 binary64))) (+.f64 x (/.f64 y #s(literal -500 binary64)))))
(.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/125000000 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y)))))
(.f64 (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y))) (.f64 (+.f64 x (/.f64 y #s(literal 500 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y))))))
(.f64 (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y))) (/.f64 (+.f64 x (/.f64 y #s(literal 500 binary64))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y)))))
(*.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal 500 binary64))))
(.f64 (+.f64 (.f64 x x) (/.f64 y (/.f64 #s(literal -250000 binary64) y))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal -500 binary64)))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/125000000 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y))))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (/.f64 y (/.f64 #s(literal -250000 binary64) y)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 y #s(literal -500 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y)))) (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (*.f64 y y)) #s(literal -1/125000000 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (*.f64 y y)) #s(literal -1/125000000 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal -500 binary64)))) (+.f64 (.f64 x x) (/.f64 y (/.f64 #s(literal -250000 binary64) y))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(literal -500 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 y (/.f64 #s(literal -250000 binary64) y)))) #s(literal -1 binary64)))
(.f64 (-.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 y #s(literal 500 binary64)) x)))
(.f64 (/.f64 (+.f64 (.f64 x x) (/.f64 y (/.f64 #s(literal -250000 binary64) y))) (+.f64 (*.f64 x x) (/.f64 y (/.f64 #s(literal -250000 binary64) y)))) (+.f64 x (/.f64 y #s(literal 500 binary64))))
(.f64 (/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/125000000 binary64))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y)) (.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (-.f64 (/.f64 y #s(literal 500 binary64)) x)))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y)) (-.f64 (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y)) (*.f64 x x)))))
(.f64 (/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/125000000 binary64))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y #s(literal 1/250000 binary64))) (.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (-.f64 (/.f64 y #s(literal 500 binary64)) x))))) (-.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y))))
(.f64 (/.f64 (+.f64 (.f64 x x) (/.f64 y (/.f64 #s(literal -250000 binary64) y))) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/125000000 binary64)))) (+.f64 (.f64 x x) (*.f64 (/.f64 y #s(literal 500 binary64)) (+.f64 x (/.f64 y #s(literal 500 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y))) (+.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 1953125000000000000000000 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 125000000 binary64)) (-.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 125000000 binary64)) (.f64 x (.f64 x x)))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) (/.f64 (-.f64 (/.f64 y #s(literal 500 binary64)) x) (/.f64 #s(literal 500 binary64) y))) (-.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 15625000000000000 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (*.f64 y y)) #s(literal -1/125000000 binary64)))))
(.f64 (pow.f64 (/.f64 (+.f64 x (/.f64 y #s(literal -500 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 15625000000000000 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 1/250000 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 1/250000 binary64))))))))
(.f64 (pow.f64 (/.f64 (+.f64 x (/.f64 y #s(literal -500 binary64))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 62500000000 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 y #s(literal 1/250000 binary64))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 500 binary64) y)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 y #s(literal 500 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 y #s(literal -500 binary64)))
(neg.f64 (/.f64 y #s(literal -500 binary64)))
(neg.f64 (*.f64 (/.f64 y #s(literal -500 binary64)) #s(literal 1 binary64)))
(/.f64 y #s(literal 500 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) y) #s(literal -500 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 500 binary64) y))
(/.f64 #s(literal 1/500 binary64) (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -500 binary64) y))
(pow.f64 (/.f64 y #s(literal 500 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 500 binary64) y) #s(literal -1 binary64))
(*.f64 y #s(literal 1/500 binary64))
(*.f64 (/.f64 y #s(literal 500 binary64)) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) y) #s(literal -1/500 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 y #s(literal 500 binary64)))
(*.f64 #s(literal 1/500 binary64) y)
(*.f64 #s(literal 1/500 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y)))
(*.f64 #s(literal 1/500 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y)) #s(literal 1 binary64)))
(*.f64 #s(literal 1/500 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 y #s(literal -500 binary64)))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 y #s(literal -500 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal -1/500 binary64) (-.f64 #s(literal 0 binary64) y))
(*.f64 #s(literal -1/500 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 1 binary64)))
(*.f64 #s(literal -1/500 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) y)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y)) #s(literal 1/500 binary64))
(*.f64 (pow.f64 (/.f64 y #s(literal 500 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 y #s(literal 500 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 1 binary64)) #s(literal -1/500 binary64))
(*.f64 (pow.f64 (pow.f64 (/.f64 y #s(literal 500 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (/.f64 y #s(literal 500 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) y)) #s(literal -1 binary64)) #s(literal -1/500 binary64))

simplify138.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

1544×	`fnmadd-define`
1404×	`fmsub-define`
1344×	`fnmsub-define`
1318×	`fma-lowering-fma.f32`
1318×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	138
1	68	120
2	160	120
3	441	120
4	1347	120
5	3754	120
6	6031	120
0	8030	120

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
(* 1/500 y)
(+ x (* 1/500 y))
(+ x (* 1/500 y))
(+ x (* 1/500 y))
x
(* x (+ 1 (* 1/500 (/ y x))))
(* x (+ 1 (* 1/500 (/ y x))))
(* x (+ 1 (* 1/500 (/ y x))))
x
(* -1 (* x (- (* -1/500 (/ y x)) 1)))
(* -1 (* x (- (* -1/500 (/ y x)) 1)))
(* -1 (* x (- (* -1/500 (/ y x)) 1)))
x
(+ x (* 1/500 y))
(+ x (* 1/500 y))
(+ x (* 1/500 y))
(* 1/500 y)
(* y (+ 1/500 (/ x y)))
(* y (+ 1/500 (/ x y)))
(* y (+ 1/500 (/ x y)))
(* 1/500 y)
(* -1 (* y (- (* -1 (/ x y)) 1/500)))
(* -1 (* y (- (* -1 (/ x y)) 1/500)))
(* -1 (* y (- (* -1 (/ x y)) 1/500)))
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)

Outputs
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(+ x (* 1/500 y))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(+ x (* 1/500 y))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(+ x (* 1/500 y))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
x
(* x (+ 1 (* 1/500 (/ y x))))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* x (+ 1 (* 1/500 (/ y x))))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* x (+ 1 (* 1/500 (/ y x))))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
x
(* -1 (* x (- (* -1/500 (/ y x)) 1)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* -1 (* x (- (* -1/500 (/ y x)) 1)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* -1 (* x (- (* -1/500 (/ y x)) 1)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
x
(+ x (* 1/500 y))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(+ x (* 1/500 y))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(+ x (* 1/500 y))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* y (+ 1/500 (/ x y)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* y (+ 1/500 (/ x y)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* y (+ 1/500 (/ x y)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* -1 (* y (- (* -1 (/ x y)) 1/500)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* -1 (* y (- (* -1 (/ x y)) 1/500)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* -1 (* y (- (* -1 (/ x y)) 1/500)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)

eval16.0ms (0.7%)

Compiler: Compiled 2711 to 308 computations (88.6% saved)

prune41.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	138	4	142

Accuracy

100.0%

Counts

142 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(fma.f64 y #s(literal 1/500 binary64) x)
✓	100.0%	(+.f64 x (/.f64 y #s(literal 500 binary64)))
▶	47.5%	(*.f64 #s(literal 1/500 binary64) y)
▶	54.2%	x

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	6272	(fma.f64 y #s(literal 1/500 binary64) x)
✓	cost-diff	0	(*.f64 #s(literal 1/500 binary64) y)

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	8	13
2	9	13
0	9	13

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
x
(* 1/500 y)
1/500
y
(+ (* y 1/500) x)
y
1/500
x

Outputs
x
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
1/500
#s(literal 1/500 binary64)
y
(+ (* y 1/500) x)
(+.f64 x (*.f64 #s(literal 1/500 binary64) y))
y
1/500
#s(literal 1/500 binary64)
x

localize45.0ms (1.9%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(fma.f64 y #s(literal 1/500 binary64) x)
✓	accuracy	99.8%	(*.f64 #s(literal 1/500 binary64) y)

Results

37.0ms

256×

valid

Compiler

Compiled 16 to 6 computations (62.5% saved)

Precisions

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

ival-mult: 4.0ms (30.2% of total)

...c/correct-round.rkt:119:19: 4.0ms (30.2% of total)

compiled-spec: 4.0ms (30.2% of total)

ival-add: 1.0ms (7.5% of total)

const: 0.0ms (0% of total)

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

series1.0ms (0%)

Counts

2 → 36

Calls

Call 1

Inputs
#<alt (* 1/500 y)>
#<alt (+ (* y 1/500) x)>

Outputs
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt (* 1/500 y)>
#<alt x>
#<alt (+ x (* 1/500 y))>
#<alt (+ x (* 1/500 y))>
#<alt (+ x (* 1/500 y))>
#<alt (* 1/500 y)>
#<alt (* y (+ 1/500 (/ x y)))>
#<alt (* y (+ 1/500 (/ x y)))>
#<alt (* y (+ 1/500 (/ x y)))>
#<alt (* 1/500 y)>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1/500)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1/500)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1/500)))>
#<alt (* 1/500 y)>
#<alt (+ x (* 1/500 y))>
#<alt (+ x (* 1/500 y))>
#<alt (+ x (* 1/500 y))>
#<alt x>
#<alt (* x (+ 1 (* 1/500 (/ y x))))>
#<alt (* x (+ 1 (* 1/500 (/ y x))))>
#<alt (* x (+ 1 (* 1/500 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/500 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1/500 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1/500 (/ y x)) 1)))>

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	y	@	inf	(* 1/500 y)
0.0ms	y	@	inf	(+ (* y 1/500) x)
0.0ms	y	@	-inf	(+ (* y 1/500) x)
0.0ms	y	@	-inf	(* 1/500 y)
0.0ms	y	@	0	(* 1/500 y)

rewrite337.0ms (14.4%)

Algorithm

1×	batch-egg-rewrite

Rules

2978×	`-lowering-.f32`
2978×	`-lowering-.f64`
2634×	`/-lowering-/.f32`
2634×	`/-lowering-/.f64`
1702×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	21	7
2	172	7
3	1897	7
0	8279	7

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 130

Calls

Call 1

Inputs
(* 1/500 y)
(+ (* y 1/500) x)

Outputs
(exp.f64 (log.f64 (*.f64 #s(literal 1/500 binary64) y)))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 1/500 binary64) y)) #s(literal 1 binary64)))
(pow.f64 (*.f64 #s(literal 1/500 binary64) y) #s(literal 1 binary64))
(*.f64 #s(literal 1/500 binary64) y)
(*.f64 #s(literal 1/500 binary64) (pow.f64 y #s(literal 1 binary64)))
(*.f64 y #s(literal 1/500 binary64))
(*.f64 (pow.f64 y #s(literal 1 binary64)) #s(literal 1/500 binary64))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 #s(literal 1/500 binary64))))
(*.f64 (exp.f64 (log.f64 #s(literal 1/500 binary64))) (exp.f64 (log.f64 y)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(+.f64 x (*.f64 #s(literal 1/500 binary64) y))
(+.f64 (/.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (-.f64 (.f64 #s(literal 1/500 binary64) y) x)) (neg.f64 (/.f64 (.f64 x x) (-.f64 (*.f64 #s(literal 1/500 binary64) y) x))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/500 binary64) y) x))) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (-.f64 (.f64 #s(literal 1/500 binary64) y) x)) (/.f64 (.f64 x x) (-.f64 (*.f64 #s(literal 1/500 binary64) y) x)))
(-.f64 (/.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (-.f64 (.f64 #s(literal 1/500 binary64) y) x)) (/.f64 (-.f64 (.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))) (-.f64 (*.f64 #s(literal 1/500 binary64) y) x)))
(-.f64 (/.f64 (.f64 x x) (+.f64 x (.f64 y #s(literal -1/500 binary64)))) (/.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (+.f64 x (*.f64 y #s(literal -1/500 binary64)))))
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(.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 #s(literal 1/500 binary64) y) x))))
(.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/500 binary64) y) x))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (.f64 x (+.f64 x (.f64 y #s(literal -1/500 binary64)))))) (+.f64 (.f64 #s(literal 1/125000000 binary64) (.f64 y (.f64 y y))) (.f64 x (.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (.f64 x (+.f64 x (.f64 y #s(literal -1/500 binary64)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/125000000 binary64) (.f64 y (.f64 y y))) (.f64 x (.f64 x x)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/500 binary64) y) x)) (-.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/500 binary64) y) x)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (*.f64 x x))) #s(literal -1 binary64)))
(.f64 (+.f64 (.f64 x x) (.f64 #s(literal -1/250000 binary64) (.f64 y y))) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y #s(literal -1/500 binary64)))))
(.f64 (/.f64 (-.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (.f64 x x)) (-.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (.f64 x x))) (+.f64 (.f64 #s(literal 1/500 binary64) y) x))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 1/125000000 binary64) (.f64 y (.f64 y y))) (.f64 x (.f64 x x))) (+.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/15625000000000000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x (.f64 y #s(literal -1/500 binary64))) (.f64 (+.f64 x (.f64 y #s(literal -1/500 binary64))) (+.f64 x (.f64 y #s(literal -1/500 binary64)))))))) (+.f64 (.f64 #s(literal 1/62500000000 binary64) (.f64 (.f64 y y) (.f64 y y))) (.f64 (.f64 x (+.f64 x (.f64 y #s(literal -1/500 binary64)))) (-.f64 (.f64 x (+.f64 x (.f64 y #s(literal -1/500 binary64)))) (.f64 #s(literal 1/250000 binary64) (*.f64 y y))))))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 1/125000000 binary64) (.f64 y (.f64 y y))) (.f64 x (.f64 x x))) (-.f64 (.f64 #s(literal 1/62500000000 binary64) (.f64 (.f64 y y) (.f64 y y))) (.f64 x (.f64 (+.f64 x (.f64 y #s(literal -1/500 binary64))) (.f64 x (+.f64 x (.f64 y #s(literal -1/500 binary64)))))))) (-.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (.f64 x (+.f64 x (*.f64 y #s(literal -1/500 binary64))))))
(.f64 (/.f64 (-.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (.f64 x x)) (-.f64 (.f64 #s(literal 1/125000000 binary64) (.f64 y (.f64 y y))) (.f64 x (.f64 x x)))) (+.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (.f64 x (+.f64 (*.f64 #s(literal 1/500 binary64) y) x))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (.f64 x (+.f64 x (.f64 y #s(literal -1/500 binary64))))) (+.f64 (.f64 #s(literal 1/1953125000000000000000000 binary64) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/15625000000000000 binary64))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/125000000 binary64) (.f64 y (.f64 y y))))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (.f64 x (+.f64 x (.f64 y #s(literal -1/500 binary64))))) (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/15625000000000000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/125000000 binary64) (.f64 y (.f64 y y))) (.f64 x (*.f64 x x)))))
(.f64 (pow.f64 (/.f64 (-.f64 (.f64 #s(literal 1/500 binary64) y) x) (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/15625000000000000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/62500000000 binary64) (.f64 (.f64 y y) (.f64 y y))) (.f64 (.f64 x x) (+.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (.f64 x x))))))
(.f64 (pow.f64 (/.f64 (-.f64 (.f64 #s(literal 1/500 binary64) y) x) (-.f64 (.f64 #s(literal 1/62500000000 binary64) (.f64 (.f64 y y) (.f64 y y))) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/250000 binary64) (.f64 y y)) (.f64 x x))))

simplify138.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

1544×	`fnmadd-define`
1404×	`fmsub-define`
1344×	`fnmsub-define`
1318×	`fma-lowering-fma.f32`
1318×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	138
1	68	120
2	160	120
3	447	120
4	1345	120
5	3744	120
6	6039	120
0	8038	120

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
(* 1/500 y)
x
(+ x (* 1/500 y))
(+ x (* 1/500 y))
(+ x (* 1/500 y))
(* 1/500 y)
(* y (+ 1/500 (/ x y)))
(* y (+ 1/500 (/ x y)))
(* y (+ 1/500 (/ x y)))
(* 1/500 y)
(* -1 (* y (- (* -1 (/ x y)) 1/500)))
(* -1 (* y (- (* -1 (/ x y)) 1/500)))
(* -1 (* y (- (* -1 (/ x y)) 1/500)))
(* 1/500 y)
(+ x (* 1/500 y))
(+ x (* 1/500 y))
(+ x (* 1/500 y))
x
(* x (+ 1 (* 1/500 (/ y x))))
(* x (+ 1 (* 1/500 (/ y x))))
(* x (+ 1 (* 1/500 (/ y x))))
x
(* -1 (* x (- (* -1/500 (/ y x)) 1)))
(* -1 (* x (- (* -1/500 (/ y x)) 1)))
(* -1 (* x (- (* -1/500 (/ y x)) 1)))

Outputs
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
x
(+ x (* 1/500 y))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(+ x (* 1/500 y))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(+ x (* 1/500 y))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* y (+ 1/500 (/ x y)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* y (+ 1/500 (/ x y)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* y (+ 1/500 (/ x y)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(* -1 (* y (- (* -1 (/ x y)) 1/500)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* -1 (* y (- (* -1 (/ x y)) 1/500)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* -1 (* y (- (* -1 (/ x y)) 1/500)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* 1/500 y)
(*.f64 #s(literal 1/500 binary64) y)
(+ x (* 1/500 y))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(+ x (* 1/500 y))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(+ x (* 1/500 y))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
x
(* x (+ 1 (* 1/500 (/ y x))))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* x (+ 1 (* 1/500 (/ y x))))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* x (+ 1 (* 1/500 (/ y x))))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
x
(* -1 (* x (- (* -1/500 (/ y x)) 1)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* -1 (* x (- (* -1/500 (/ y x)) 1)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)
(* -1 (* x (- (* -1/500 (/ y x)) 1)))
(+.f64 (*.f64 #s(literal 1/500 binary64) y) x)

eval18.0ms (0.8%)

Compiler: Compiled 5163 to 417 computations (91.9% saved)

prune47.0ms (2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	166	4	170

Accuracy

100.0%

Counts

170 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 y #s(literal 1/500 binary64) x)
✓	100.0%	(+.f64 x (/.f64 y #s(literal 500 binary64)))
✓	47.5%	(*.f64 #s(literal 1/500 binary64) y)
✓	54.2%	x

Compiler

Compiled 36 to 23 computations (36.1% saved)

regimes10.0ms (0.4%)

Counts

4 → 1

Calls

Call 1

Inputs
x
(*.f64 #s(literal 1/500 binary64) y)
(+.f64 x (/.f64 y #s(literal 500 binary64)))
(fma.f64 y #s(literal 1/500 binary64) x)

Outputs
(+.f64 x (/.f64 y #s(literal 500 binary64)))

Calls

4 calls:

3.0ms	y
2.0ms	(+.f64 x (/.f64 y #s(literal 500 binary64)))
2.0ms	(/.f64 y #s(literal 500 binary64))
2.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(+.f64 x (/.f64 y #s(literal 500 binary64)))`
100.0%	1	`(/.f64 y #s(literal 500 binary64))`

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes3.0ms (0.1%)

Counts

2 → 3

Calls

Call 1

Inputs
x
(*.f64 #s(literal 1/500 binary64) y)

Outputs
x
(*.f64 #s(literal 1/500 binary64) y)
x

Calls

2 calls:

2.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
78.9%	3	`x`
77.9%	3	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0.1%)

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
54.2%	1	`y`
54.2%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch26.0ms (1.1%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
11.0ms	27351.325941641677	6869642.511740002
14.0ms	-2.595035637807251e-73	-5.063212630901755e-98

Results

12.0ms

288×

valid

Compiler

Compiled 192 to 153 computations (20.3% saved)

Precisions

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

ival-div: 2.0ms (46.3% of total)

ival-add: 1.0ms (23.2% of total)

const: 0.0ms (0% of total)

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

simplify9.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	18	19

Stop Event

1×

saturated

Calls

Call 1

Inputs

(+.f64 x (/.f64 y #s(literal 500 binary64)))

(if (<=.f64 x #s(literal -4058157609103859/15914343565113172548972231940698266883214596825515126958094847260581103904401068017057792 binary64)) x (if (<=.f64 x #s(literal 110000 binary64)) (*.f64 #s(literal 1/500 binary64) y) x))

Outputs
(+.f64 x (/.f64 y #s(literal 500 binary64)))
(if (<=.f64 x #s(literal -4058157609103859/15914343565113172548972231940698266883214596825515126958094847260581103904401068017057792 binary64)) x (if (<=.f64 x #s(literal 110000 binary64)) (*.f64 #s(literal 1/500 binary64) y) x))
(if (<=.f64 x #s(literal -4058157609103859/15914343565113172548972231940698266883214596825515126958094847260581103904401068017057792 binary64)) x (if (<=.f64 x #s(literal 110000 binary64)) (*.f64 y #s(literal 1/500 binary64)) x))
x

soundness390.0ms (16.6%)

Rules

1544×	`fnmadd-define`
1404×	`fmsub-define`
1344×	`fnmsub-define`
1318×	`fma-lowering-fma.f32`
1318×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	138
1	68	120
2	160	120
3	441	120
4	1347	120
5	3754	120
6	6031	120
0	8030	120

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 32 to 21 computations (34.4% saved)

preprocess24.0ms (1%)

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

Data.Colour.CIE:cieLAB from colour-2.3.3, C

analyze0.0ms (0%)

sample701.0ms (29.9%)

preprocess33.0ms (1.4%)

explain47.0ms (2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.2%)

localize22.0ms (0.9%)

series2.0ms (0.1%)

rewrite286.0ms (12.2%)

simplify138.0ms (5.9%)

eval16.0ms (0.7%)

prune41.0ms (1.7%)

simplify5.0ms (0.2%)

localize45.0ms (1.9%)

series1.0ms (0%)

rewrite337.0ms (14.4%)

simplify138.0ms (5.9%)

eval18.0ms (0.8%)

prune47.0ms (2%)

regimes10.0ms (0.4%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch26.0ms (1.1%)

simplify9.0ms (0.4%)

soundness390.0ms (16.6%)

preprocess24.0ms (1%)

end0.0ms (0%)

Profiling