Optimisation.CirclePacking:place from circle-packing-0.1.0.4, A

Time bar (total: 4.9s)

analyze31.0ms (0.6%)

Memory
-29.8MiB live, 48.7MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%99.9%0.1%0%0%0%2
25%25%74.9%0.1%0%0%0%3
28.6%25%62.4%0.1%0%12.5%0%4
46.2%37.5%43.7%0.1%0%18.7%0%5
52.2%37.5%34.3%0.1%0%28.1%0%6
65.1%43.7%23.4%0.1%0%32.8%0%7
70.9%43.7%18%0.1%0%38.2%0%8
79.5%46.8%12.1%0.1%0%41%0%9
83.6%46.8%9.2%0.1%0%43.9%0%10
88.7%48.4%6.1%0.1%0%45.4%0%11
91.3%48.4%4.6%0.1%0%46.9%0%12
Compiler

Compiled 6 to 6 computations (0% saved)

sample659.0ms (13.4%)

Memory
-4.7MiB live, 965.7MiB allocated
Samples
316.0ms8 256×0valid
18.0ms515×0invalid
Precisions
Click to see histograms. Total time spent on operations: 141.0ms
ival-add: 65.0ms (46.2% of total)
ival-sqrt: 65.0ms (46.2% of total)
ival-true: 6.0ms (4.3% of total)
ival-assert: 4.0ms (2.8% of total)
Bogosity

preprocess18.0ms (0.4%)

Memory
-7.1MiB live, 34.6MiB allocated
Algorithm
egg-herbie
Rules
44×sub-neg
32×associate--r+
24×neg-mul-1
22×cancel-sign-sub-inv
22×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01428
12726
24226
36426
412326
516226
620126
721226
821426
044
154
054
Stop Event
iter limit
saturated
saturated
Calls
Call 1
Inputs
(sqrt (+ x y))
Outputs
(sqrt (+ x y))
(sqrt.f64 (+.f64 x y))
Call 2
Inputs
(sqrt (+ x y))
(sqrt (+ (neg x) y))
(sqrt (+ x (neg y)))
(neg (sqrt (+ (neg x) y)))
(neg (sqrt (+ x (neg y))))
(sqrt (+ y x))
Outputs
(sqrt (+ x y))
(sqrt (+ (neg x) y))
(sqrt (- y x))
(sqrt (+ x (neg y)))
(sqrt (- x y))
(neg (sqrt (+ (neg x) y)))
(neg (sqrt (- y x)))
(neg (sqrt (+ x (neg y))))
(neg (sqrt (- x y)))
(sqrt (+ y x))
(sqrt (+ x y))
Symmetry

(sort x y)

explain42.0ms (0.9%)

Memory
27.0MiB live, 103.9MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(sqrt.f64 (+.f64 x y))
00-0-y
00-0-(+.f64 x y)
00-0-x
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
18.0ms512×0valid
Compiler

Compiled 34 to 20 computations (41.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-sqrt: 4.0ms (54.4% of total)
ival-add: 3.0ms (40.8% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
1.8MiB live, 1.8MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(sqrt.f64 (+.f64 x y))
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify5.0ms (0.1%)

Memory
-29.5MiB live, 8.7MiB allocated
Algorithm
egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 x y)
cost-diff0
(sqrt.f64 (+.f64 x y))
Rules
+-lowering-+.f64
+-lowering-+.f32
sqrt-lowering-sqrt.f64
sqrt-lowering-sqrt.f32
+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049
159
059
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(sqrt (+ x y))
(+ x y)
x
y
Outputs
(sqrt (+ x y))
(sqrt.f64 (+.f64 x y))
(+ x y)
(+.f64 x y)
x
y

localize14.0ms (0.3%)

Memory
34.9MiB live, 34.9MiB allocated
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(+.f64 x y)
accuracy100.0%
(sqrt.f64 (+.f64 x y))
Samples
9.0ms256×0valid
Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-add: 2.0ms (55.3% of total)
ival-sqrt: 2.0ms (55.3% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series12.0ms (0.2%)

Memory
-25.9MiB live, 13.8MiB allocated
Counts
2 → 48
Calls
Call 1
Inputs
#<alt (sqrt (+ x y))>
#<alt (+ x y)>
Outputs
#<alt (sqrt y)>
#<alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))>
#<alt (+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))>
#<alt (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))>
#<alt (sqrt y)>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))>
#<alt y>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt x>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt x>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt y>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
Calls

12 calls:

TimeVariablePointExpression
7.0ms
x
@-inf
(sqrt (+ x y))
1.0ms
y
@-inf
(sqrt (+ x y))
1.0ms
x
@inf
(sqrt (+ x y))
1.0ms
y
@inf
(sqrt (+ x y))
0.0ms
y
@0
(sqrt (+ x y))

rewrite629.0ms (12.8%)

Memory
-1.4MiB live, 518.0MiB allocated
Algorithm
batch-egg-rewrite
Rules
5 128×accelerator-lowering-fma.f32
5 128×accelerator-lowering-fma.f64
4 292×/-lowering-/.f32
4 292×/-lowering-/.f64
3 378×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047
1207
21437
313627
083027
Stop Event
iter limit
node limit
Counts
2 → 226
Calls
Call 1
Inputs
(sqrt (+ x y))
(+ x y)
Outputs
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 x y))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 x y) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 x y) (+.f64 x y))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 (+.f64 x y)) #s(literal 1/4 binary64) (*.f64 (log.f64 (+.f64 x y)) #s(literal 1/4 binary64))))
(hypot.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 x y))
(/.f64 (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (sqrt.f64 (fma.f64 x (-.f64 x y) (*.f64 y y))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 x y))) (sqrt.f64 (-.f64 x y)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 y x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))))) (sqrt.f64 (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (fma.f64 (*.f64 y (*.f64 y y)) (-.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))))) (sqrt.f64 (*.f64 (fma.f64 (*.f64 y (*.f64 y y)) (-.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (fma.f64 x (-.f64 x y) (*.f64 y y)))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)))) (sqrt.f64 (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)))) (sqrt.f64 (*.f64 (-.f64 x y) (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (*.f64 x (*.f64 x (*.f64 x x)))))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)))) (sqrt.f64 (*.f64 (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)) (fma.f64 x (-.f64 x y) (*.f64 y y)))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)))) (sqrt.f64 (*.f64 (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (*.f64 x (*.f64 x (*.f64 x x)))) (-.f64 x y))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (+.f64 x y) (-.f64 x y)))) (sqrt.f64 (*.f64 (-.f64 x y) (fma.f64 x x (*.f64 y y)))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (+.f64 x y) (-.f64 x y)))) (sqrt.f64 (*.f64 (fma.f64 x x (*.f64 y y)) (-.f64 x y))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (-.f64 x y) (*.f64 y y)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 x y) (-.f64 x y)))) (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) y)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 y x))) (sqrt.f64 (-.f64 y x)))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 x y)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 x y))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x y)))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x y)) (*.f64 (-.f64 x y) (*.f64 y y)))) (sqrt.f64 (*.f64 (-.f64 x y) (-.f64 x y))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 x y) (-.f64 y x)))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 y x))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x y)) (*.f64 (*.f64 x x) (*.f64 (/.f64 x (-.f64 x y)) (/.f64 x (-.f64 x y))))) (*.f64 (*.f64 y (/.f64 y (-.f64 x y))) (*.f64 (*.f64 y y) (*.f64 (/.f64 y (-.f64 x y)) (/.f64 y (-.f64 x y))))))) (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 (/.f64 x (-.f64 x y)) (/.f64 x (-.f64 x y))) (fma.f64 (*.f64 y y) (*.f64 (/.f64 y (-.f64 x y)) (/.f64 y (-.f64 x y))) (*.f64 (/.f64 (*.f64 x x) (-.f64 x y)) (*.f64 y (/.f64 y (-.f64 x y))))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (/.f64 x (-.f64 x y)) (/.f64 x (-.f64 x y)))) (*.f64 (*.f64 y y) (*.f64 (/.f64 y (-.f64 x y)) (/.f64 y (-.f64 x y)))))) (sqrt.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (*.f64 y (/.f64 y (-.f64 x y))))))
(/.f64 (sqrt.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))))) (fma.f64 x (-.f64 x y) (*.f64 y y)))) (sqrt.f64 (fma.f64 (*.f64 y (*.f64 y y)) (-.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))) (fma.f64 x (-.f64 x y) (*.f64 y y)))) (sqrt.f64 (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))) (-.f64 x y))) (sqrt.f64 (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (*.f64 x (*.f64 x (*.f64 x x))))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (+.f64 x y) (-.f64 x y))) (-.f64 x y))) (sqrt.f64 (fma.f64 x x (*.f64 y y))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (-.f64 x y) (*.f64 y y))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 x y) (-.f64 x y))))) (neg.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) y))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 y x)))) (neg.f64 (sqrt.f64 (-.f64 y x))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 x (-.f64 x y) (*.f64 y y))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 x y))))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 x y)))))
(pow.f64 (+.f64 x y) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (+.f64 x y) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 x y) (+.f64 x y)) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y))) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (+.f64 x y)))
(*.f64 (sqrt.f64 (+.f64 x y)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (+.f64 x y)) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x y) (*.f64 y y)))))
(*.f64 (sqrt.f64 (fma.f64 x (-.f64 x y) (*.f64 y y))) (pow.f64 (/.f64 (+.f64 x y) (fma.f64 x (-.f64 x y) (*.f64 y y))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x (-.f64 x y) (*.f64 y y))) (sqrt.f64 (/.f64 (+.f64 x y) (fma.f64 x (-.f64 x y) (*.f64 y y)))))
(*.f64 (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 x y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x y)))
(*.f64 (pow.f64 (+.f64 x y) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x y) #s(literal 1/4 binary64)))
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(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 x y) (-.f64 y x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 y x))))
(*.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x y)) (*.f64 (*.f64 x x) (*.f64 (/.f64 x (-.f64 x y)) (/.f64 x (-.f64 x y))))) (*.f64 (*.f64 y (/.f64 y (-.f64 x y))) (*.f64 (*.f64 y y) (*.f64 (/.f64 y (-.f64 x y)) (/.f64 y (-.f64 x y)))))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 (/.f64 x (-.f64 x y)) (/.f64 x (-.f64 x y))) (fma.f64 (*.f64 y y) (*.f64 (/.f64 y (-.f64 x y)) (/.f64 y (-.f64 x y))) (*.f64 (/.f64 (*.f64 x x) (-.f64 x y)) (*.f64 y (/.f64 y (-.f64 x y))))))))
(*.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (/.f64 x (-.f64 x y)) (/.f64 x (-.f64 x y)))) (*.f64 (*.f64 y y) (*.f64 (/.f64 y (-.f64 x y)) (/.f64 y (-.f64 x y))))) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 x (-.f64 x y)) (*.f64 y (/.f64 y (-.f64 x y))))))
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))))) (fma.f64 x (-.f64 x y) (*.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y (*.f64 y y)) (-.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))))
(*.f64 (/.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))) (fma.f64 x (-.f64 x y) (*.f64 y y))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))))
(*.f64 (/.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (*.f64 x (*.f64 x (*.f64 x x))))))
(*.f64 (/.f64 (*.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (+.f64 x y) (-.f64 x y))) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 y y))))
(*.f64 (/.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 y (*.f64 y y)) (*.f64 (-.f64 y x) (*.f64 (-.f64 y x) (-.f64 y x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (fma.f64 (*.f64 y (-.f64 y x)) (fma.f64 y (-.f64 y x) (-.f64 #s(literal 0 binary64) (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))))
(*.f64 (/.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (-.f64 (*.f64 x x) (*.f64 y (-.f64 y x))))) (-.f64 (*.f64 x x) (*.f64 y (-.f64 y x))))
(*.f64 (/.f64 (*.f64 (+.f64 x y) (-.f64 x y)) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))) (fma.f64 x x (*.f64 y (+.f64 x y))))
(*.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y (*.f64 y y)) (-.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))))
(*.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))))
(*.f64 (pow.f64 (/.f64 (-.f64 x y) (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (*.f64 x (*.f64 x (*.f64 x x))))))
(*.f64 (pow.f64 (/.f64 (-.f64 x y) (*.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (+.f64 x y) (-.f64 x y)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 y y))))
(*.f64 (exp.f64 (log.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))))) (exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 (fma.f64 x (-.f64 x y) (*.f64 y y))))))
(*.f64 (exp.f64 (log.f64 (*.f64 (+.f64 x y) (-.f64 x y)))) (exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 (-.f64 x y)))))

simplify1.6s (32%)

Memory
-10.4MiB live, 1 000.6MiB allocated
Algorithm
egg-herbie
Rules
28 536×accelerator-lowering-fma.f32
28 536×accelerator-lowering-fma.f64
5 638×*-lowering-*.f32
5 638×*-lowering-*.f64
2 832×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0156630
1454600
21425582
34619570
08274534
Stop Event
iter limit
node limit
Counts
48 → 48
Calls
Call 1
Inputs
(sqrt y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(sqrt x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
y
(+ x y)
(+ x y)
(+ x y)
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
x
(+ x y)
(+ x y)
(+ x y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
Outputs
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(fma.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))) (*.f64 x #s(literal -1/8 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (sqrt.f64 y))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(fma.f64 x (fma.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 x #s(literal 1/16 binary64)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (sqrt.f64 y))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(*.f64 x (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 y #s(literal -1/8 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
(*.f64 x (fma.f64 (*.f64 y y) (fma.f64 y (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 y #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 x (fma.f64 y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 y #s(literal -1/8 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 y #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 y (*.f64 y #s(literal -1/8 binary64))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (*.f64 y (*.f64 y y)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 y #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 y (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 y #s(literal -1/8 binary64)))) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(fma.f64 y (fma.f64 y (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 y #s(literal 1/16 binary64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (sqrt.f64 x))
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(*.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(*.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(*.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (*.f64 x (*.f64 #s(literal 1/16 binary64) (*.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(*.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))) (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(*.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))) (*.f64 x #s(literal -1/2 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(*.f64 y (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 x x)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (/.f64 (*.f64 x (*.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))) (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
y
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
x
(* x (+ 1 (/ y x)))
(+.f64 y x)
(* x (+ 1 (/ y x)))
(+.f64 y x)
(* x (+ 1 (/ y x)))
(+.f64 y x)
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 y x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 y x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 y x)
x
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
y
(* y (+ 1 (/ x y)))
(+.f64 y x)
(* y (+ 1 (/ x y)))
(+.f64 y x)
(* y (+ 1 (/ x y)))
(+.f64 y x)
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 y x)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 y x)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 y x)

eval33.0ms (0.7%)

Memory
17.4MiB live, 95.3MiB allocated
Compiler

Compiled 7 918 to 856 computations (89.2% saved)

prune46.0ms (0.9%)

Memory
-16.0MiB live, 99.7MiB allocated
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2713274
Fresh000
Picked011
Done000
Total2714275
Accuracy
100.0%
Counts
275 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.5%
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y))
99.5%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y))))
100.0%
(sqrt.f64 (+.f64 x y))
97.1%
(sqrt.f64 y)
Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify5.0ms (0.1%)

Memory
12.1MiB live, 12.1MiB allocated
Algorithm
egg-herbie
Localize:

Found 9 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(literal 1/2 binary64) x)
cost-diff0
(/.f64 #s(literal 1 binary64) y)
cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
cost-diff0
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y))
cost-diff0
(+.f64 x y)
cost-diff0
(/.f64 #s(literal 1 binary64) (+.f64 x y))
cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)))
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y))))
cost-diff0
(sqrt.f64 y)
Rules
24×*-lowering-*.f32
24×*-lowering-*.f64
12×accelerator-lowering-fma.f32
12×accelerator-lowering-fma.f64
10×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01455
12255
22955
33155
03154
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(sqrt y)
y
(/ 1 (sqrt (/ 1 (+ x y))))
1
(sqrt (/ 1 (+ x y)))
(/ 1 (+ x y))
(+ x y)
x
y
(+ (* (sqrt (/ 1 y)) (* 1/2 x)) (sqrt y))
(sqrt (/ 1 y))
(/ 1 y)
1
y
(* 1/2 x)
1/2
x
(sqrt y)
Outputs
(sqrt y)
(sqrt.f64 y)
y
(/ 1 (sqrt (/ 1 (+ x y))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x))))
1
#s(literal 1 binary64)
(sqrt (/ 1 (+ x y)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)))
(/ 1 (+ x y))
(/.f64 #s(literal 1 binary64) (+.f64 y x))
(+ x y)
(+.f64 y x)
x
y
(+ (* (sqrt (/ 1 y)) (* 1/2 x)) (sqrt y))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
1
#s(literal 1 binary64)
y
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
x
(sqrt y)
(sqrt.f64 y)

localize63.0ms (1.3%)

Memory
-4.7MiB live, 116.1MiB allocated
Localize:

Found 9 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(*.f64 #s(literal 1/2 binary64) x)
accuracy100.0%
(sqrt.f64 y)
accuracy100.0%
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y))
accuracy99.8%
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
accuracy100.0%
(+.f64 x y)
accuracy100.0%
(/.f64 #s(literal 1 binary64) (+.f64 x y))
accuracy99.8%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)))
accuracy99.5%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y))))
accuracy100.0%
(sqrt.f64 y)
Samples
27.0ms256×0valid
Compiler

Compiled 56 to 16 computations (71.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 16.0ms
ival-div: 5.0ms (30.4% of total)
ival-sqrt: 5.0ms (30.4% of total)
ival-mult: 3.0ms (18.2% of total)
ival-add: 2.0ms (12.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series14.0ms (0.3%)

Memory
-3.2MiB live, 35.2MiB allocated
Counts
9 → 168
Calls
Call 1
Inputs
#<alt (sqrt y)>
#<alt (/ 1 (sqrt (/ 1 (+ x y))))>
#<alt (sqrt (/ 1 (+ x y)))>
#<alt (/ 1 (+ x y))>
#<alt (+ x y)>
#<alt (+ (* (sqrt (/ 1 y)) (* 1/2 x)) (sqrt y))>
#<alt (sqrt (/ 1 y))>
#<alt (/ 1 y)>
#<alt (* 1/2 x)>
Outputs
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (sqrt y)>
#<alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))>
#<alt (+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))>
#<alt (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))>
#<alt (sqrt y)>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))>
#<alt (sqrt (/ 1 y))>
#<alt (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))>
#<alt (+ (sqrt (/ 1 y)) (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* 3/8 (* x (sqrt (/ 1 (pow y 5))))))))>
#<alt (+ (sqrt (/ 1 y)) (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* x (+ (* -5/16 (* x (sqrt (/ 1 (pow y 7))))) (* 3/8 (sqrt (/ 1 (pow y 5)))))))))>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2)))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* 1/4 (* x (pow y 2))) (pow y 3)))) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2))))))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (pow y 2))) (* 1/2 (* (sqrt (/ 1 x)) (+ (* -1/4 (/ (* x (pow y 2)) (pow (sqrt -1) 2))) (pow y 3))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)))>
#<alt (+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 3/8 (* (sqrt (/ 1 (pow x 5))) y)))))>
#<alt (+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* y (+ (* -5/16 (* (sqrt (/ 1 (pow x 7))) y)) (* 3/8 (sqrt (/ 1 (pow x 5)))))))))>
#<alt (sqrt (/ 1 y))>
#<alt (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))>
#<alt (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))>
#<alt (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 2) y)) (pow x 3)))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))>
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))>
#<alt (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))>
#<alt (+ (* -1 (/ (+ (* -1/2 (* (pow x 2) (sqrt y))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1/4 (/ (* (pow x 2) y) (pow (sqrt -1) 2))) (pow x 3))))) (pow y 3))) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))>
#<alt (/ 1 y)>
#<alt (+ (* -1 (/ x (pow y 2))) (/ 1 y))>
#<alt (+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))>
#<alt (+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1 (/ y x))) x)>
#<alt (/ (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) x)>
#<alt (/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ y x) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow y 2) x) y) x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (pow y 2)) x)) y) x)) 1) x))>
#<alt (/ 1 x)>
#<alt (+ (* -1 (/ y (pow x 2))) (/ 1 x))>
#<alt (+ (* y (- (/ y (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x))>
#<alt (+ (* y (- (* y (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))>
#<alt (/ 1 y)>
#<alt (/ (+ 1 (* -1 (/ x y))) y)>
#<alt (/ (- (+ 1 (/ (pow x 2) (pow y 2))) (/ x y)) y)>
#<alt (/ (- (+ 1 (* -1 (/ (pow x 3) (pow y 3)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))) y)>
#<alt (/ 1 y)>
#<alt (* -1 (/ (- (/ x y) 1) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) x) y)) 1) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y)) x) y)) 1) y))>
#<alt y>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt x>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt x>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt y>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)>
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)>
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)>
#<alt (sqrt y)>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (sqrt y)>
#<alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))>
#<alt (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))>
#<alt (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
Calls

42 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(sqrt (/ 1 (+ x y)))
1.0ms
y
@-inf
(/ 1 (+ x y))
1.0ms
x
@0
(+ (* (sqrt (/ 1 y)) (* 1/2 x)) (sqrt y))
1.0ms
y
@-inf
(sqrt (/ 1 (+ x y)))
1.0ms
x
@inf
(sqrt (/ 1 (+ x y)))

rewrite251.0ms (5.1%)

Memory
10.0MiB live, 566.7MiB allocated
Algorithm
batch-egg-rewrite
Rules
4 850×accelerator-lowering-fma.f32
4 850×accelerator-lowering-fma.f64
3 186×*-lowering-*.f32
3 186×*-lowering-*.f64
1 918×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01445
17437
248237
0462736
Stop Event
iter limit
iter limit
node limit
Counts
9 → 483
Calls
Call 1
Inputs
(sqrt y)
(/ 1 (sqrt (/ 1 (+ x y))))
(sqrt (/ 1 (+ x y)))
(/ 1 (+ x y))
(+ x y)
(+ (* (sqrt (/ 1 y)) (* 1/2 x)) (sqrt y))
(sqrt (/ 1 y))
(/ 1 y)
(* 1/2 x)
Outputs
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 y)))
(fabs.f64 (sqrt.f64 y))
(sqrt.f64 y)
(/.f64 (sqrt.f64 y) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) y)) (sqrt.f64 #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 y)) #s(literal -1 binary64))
(pow.f64 y #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 y) #s(literal 1 binary64))
(pow.f64 (*.f64 y y) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (sqrt.f64 y) #s(literal 1 binary64))
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64)))
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (/.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 y)) (sqrt.f64 (sqrt.f64 y)))
(exp.f64 (*.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 y x)) #s(literal 0 binary64))))
(exp.f64 (*.f64 (log.f64 (+.f64 y x)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 (+.f64 y x))) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 y x)) #s(literal 0 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 y x))))
(sqrt.f64 (+.f64 y x))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 y x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 y y (*.f64 x (-.f64 x y)))) (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 x y)) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 x y)))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 y x))))
(/.f64 (sqrt.f64 (+.f64 y x)) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 y x))) (sqrt.f64 #s(literal -1 binary64)))
(/.f64 (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (sqrt.f64 (fma.f64 y y (*.f64 x (-.f64 x y)))))
(/.f64 (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 y y (*.f64 x (-.f64 x y))))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (sqrt.f64 (-.f64 x y)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 x y))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 y x))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 x (-.f64 x y))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 y x) (-.f64 x y)))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 x y))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x)))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))))) (neg.f64 (sqrt.f64 (fma.f64 y y (*.f64 x (-.f64 x y))))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 x y)))) (neg.f64 (sqrt.f64 (-.f64 x y))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))))) (sqrt.f64 (fma.f64 y y (*.f64 x (-.f64 x y)))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 x y)))) (sqrt.f64 (-.f64 x y)))
(/.f64 (*.f64 (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 y y (*.f64 x (-.f64 x y)))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 x y))) #s(literal 1 binary64)) (sqrt.f64 (-.f64 x y)))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 y x) #s(literal -1/4 binary64))) (pow.f64 (+.f64 y x) #s(literal -1/4 binary64)))
(pow.f64 (+.f64 y x) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x))) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (+.f64 y x)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 y x)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 y x))))
(*.f64 (sqrt.f64 (+.f64 y x)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (+.f64 y x)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
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(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y))
(*.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))
(*.f64 (pow.f64 y #s(literal -1/4 binary64)) (*.f64 (pow.f64 y #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (pow.f64 y #s(literal -1/4 binary64))) (pow.f64 y #s(literal -1/4 binary64)))
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 y) x)) (sqrt.f64 y))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 y) x))) (sqrt.f64 y))
(/.f64 (*.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 y) x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 y)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 y) x))) (sqrt.f64 (-.f64 #s(literal 0 binary64) y)))
(*.f64 (sqrt.f64 y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y)))
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) (sqrt.f64 y)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 y) x)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64)))
(*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))
(*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (*.f64 (sqrt.f64 y) x)))
(*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y)) (sqrt.f64 y))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) (*.f64 (sqrt.f64 y) x))
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (*.f64 (pow.f64 y #s(literal 1/4 binary64)) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y))))
(*.f64 (pow.f64 y #s(literal -1/4 binary64)) (*.f64 (pow.f64 y #s(literal -1/4 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 y) x))))
(*.f64 (/.f64 x (sqrt.f64 y)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 y)))
(*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 y) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))
(*.f64 (*.f64 (sqrt.f64 y) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y)))
(*.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(*.f64 (*.f64 (sqrt.f64 y) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 y)))
(*.f64 (*.f64 (sqrt.f64 y) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y))) x)
(*.f64 (*.f64 (sqrt.f64 y) (/.f64 x (sqrt.f64 y))) #s(literal 1/2 binary64))
(*.f64 (*.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y)) (pow.f64 y #s(literal 1/4 binary64))) (pow.f64 y #s(literal 1/4 binary64)))

simplify499.0ms (10.1%)

Memory
15.9MiB live, 795.2MiB allocated
Algorithm
egg-herbie
Rules
13 426×accelerator-lowering-fma.f32
13 426×accelerator-lowering-fma.f64
4 642×*-lowering-*.f32
4 642×*-lowering-*.f64
4 014×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03592044
110741931
232881839
376031839
087451732
Stop Event
iter limit
node limit
Counts
168 → 168
Calls
Call 1
Inputs
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(sqrt x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(sqrt (/ 1 y))
(+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))
(+ (sqrt (/ 1 y)) (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* 3/8 (* x (sqrt (/ 1 (pow y 5))))))))
(+ (sqrt (/ 1 y)) (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* x (+ (* -5/16 (* x (sqrt (/ 1 (pow y 7))))) (* 3/8 (sqrt (/ 1 (pow y 5)))))))))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2)))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* 1/4 (* x (pow y 2))) (pow y 3)))) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2))))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (pow y 2))) (* 1/2 (* (sqrt (/ 1 x)) (+ (* -1/4 (/ (* x (pow y 2)) (pow (sqrt -1) 2))) (pow y 3))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)))
(+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 3/8 (* (sqrt (/ 1 (pow x 5))) y)))))
(+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* y (+ (* -5/16 (* (sqrt (/ 1 (pow x 7))) y)) (* 3/8 (sqrt (/ 1 (pow x 5)))))))))
(sqrt (/ 1 y))
(+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 2) y)) (pow x 3)))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (* (pow x 2) (sqrt y))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1/4 (/ (* (pow x 2) y) (pow (sqrt -1) 2))) (pow x 3))))) (pow y 3))) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(/ 1 y)
(+ (* -1 (/ x (pow y 2))) (/ 1 y))
(+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))
(+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))
(/ 1 x)
(/ (+ 1 (* -1 (/ y x))) x)
(/ (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) x)
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) x)
(/ 1 x)
(* -1 (/ (- (/ y x) 1) x))
(* -1 (/ (- (* -1 (/ (- (/ (pow y 2) x) y) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (pow y 2)) x)) y) x)) 1) x))
(/ 1 x)
(+ (* -1 (/ y (pow x 2))) (/ 1 x))
(+ (* y (- (/ y (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x))
(+ (* y (- (* y (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))
(/ 1 y)
(/ (+ 1 (* -1 (/ x y))) y)
(/ (- (+ 1 (/ (pow x 2) (pow y 2))) (/ x y)) y)
(/ (- (+ 1 (* -1 (/ (pow x 3) (pow y 3)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))) y)
(/ 1 y)
(* -1 (/ (- (/ x y) 1) y))
(* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) x) y)) 1) y))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y)) x) y)) 1) y))
y
(+ x y)
(+ x y)
(+ x y)
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
x
(+ x y)
(+ x y)
(+ x y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* 1/2 (* x (sqrt (/ 1 y))))
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(sqrt y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
Outputs
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 y))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(fma.f64 x (fma.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 x #s(literal 1/16 binary64)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (sqrt.f64 y))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(*.f64 x (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
(*.f64 x (fma.f64 (*.f64 y y) (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) y (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (fma.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 y y)) #s(literal 1/8 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 y #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (*.f64 y (*.f64 y y)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 y y)) #s(literal 1/8 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 y (fma.f64 y (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(fma.f64 y (fma.f64 y (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 y #s(literal 1/16 binary64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (sqrt.f64 x))
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(*.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(*.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
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(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y))
(* 1/2 (* x (sqrt (/ 1 y))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)

eval89.0ms (1.8%)

Memory
17.2MiB live, 182.0MiB allocated
Compiler

Compiled 12 902 to 1 867 computations (85.5% saved)

prune81.0ms (1.6%)

Memory
10.5MiB live, 201.2MiB allocated
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New6762678
Fresh000
Picked123
Done011
Total6775682
Accuracy
100.0%
Counts
682 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.5%
(fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))
99.5%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y))))
96.7%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
100.0%
(sqrt.f64 (+.f64 x y))
97.1%
(sqrt.f64 y)
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify4.0ms (0.1%)

Memory
7.2MiB live, 7.2MiB allocated
Algorithm
egg-herbie
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 y)
cost-diff0
(/.f64 x (sqrt.f64 y))
cost-diff0
(fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))
cost-diff0
(/.f64 #s(literal 1 binary64) y)
cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
Rules
12×*-lowering-*.f32
12×*-lowering-*.f64
10×/-lowering-/.f32
10×/-lowering-/.f64
accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01133
11733
22133
32233
02232
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(/ 1 (sqrt (/ 1 y)))
1
(sqrt (/ 1 y))
(/ 1 y)
y
(+ (* (/ x (sqrt y)) 1/2) (sqrt y))
(/ x (sqrt y))
x
(sqrt y)
y
1/2
Outputs
(/ 1 (sqrt (/ 1 y)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
1
#s(literal 1 binary64)
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
y
(+ (* (/ x (sqrt y)) 1/2) (sqrt y))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) (sqrt.f64 y))
(/ x (sqrt y))
(/.f64 x (sqrt.f64 y))
x
(sqrt y)
(sqrt.f64 y)
y
1/2
#s(literal 1/2 binary64)

localize39.0ms (0.8%)

Memory
-22.1MiB live, 58.8MiB allocated
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(sqrt.f64 y)
accuracy100.0%
(fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))
accuracy99.7%
(/.f64 x (sqrt.f64 y))
accuracy100.0%
(/.f64 #s(literal 1 binary64) y)
accuracy99.8%
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
accuracy99.5%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
Samples
22.0ms256×0valid
Compiler

Compiled 34 to 13 computations (61.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 14.0ms
ival-div: 5.0ms (35.5% of total)
ival-add: 3.0ms (21.3% of total)
ival-sqrt: 3.0ms (21.3% of total)
ival-mult: 2.0ms (14.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory
7.4MiB live, 7.4MiB allocated
Counts
6 → 96
Calls
Call 1
Inputs
#<alt (/ 1 (sqrt (/ 1 y)))>
#<alt (sqrt (/ 1 y))>
#<alt (/ 1 y)>
#<alt (+ (* (/ x (sqrt y)) 1/2) (sqrt y))>
#<alt (/ x (sqrt y))>
#<alt (sqrt y)>
Outputs
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (* -1 (sqrt y))>
#<alt (* -1 (sqrt y))>
#<alt (* -1 (sqrt y))>
#<alt (* -1 (sqrt y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (sqrt y)>
#<alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))>
#<alt (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))>
#<alt (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)>
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)>
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)>
#<alt (sqrt y)>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (* x (sqrt (/ 1 y)))>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
Calls

24 calls:

TimeVariablePointExpression
1.0ms
y
@-inf
(/ 1 (sqrt (/ 1 y)))
1.0ms
y
@-inf
(+ (* (/ x (sqrt y)) 1/2) (sqrt y))
0.0ms
x
@0
(/ x (sqrt y))
0.0ms
y
@-inf
(/ x (sqrt y))
0.0ms
x
@-inf
(/ x (sqrt y))

rewrite202.0ms (4.1%)

Memory
-43.0MiB live, 345.8MiB allocated
Algorithm
batch-egg-rewrite
Rules
3 576×accelerator-lowering-fma.f32
3 576×accelerator-lowering-fma.f64
2 440×*-lowering-*.f32
2 440×*-lowering-*.f64
1 744×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01132
15423
233323
0411722
Stop Event
iter limit
iter limit
node limit
Counts
6 → 298
Calls
Call 1
Inputs
(/ 1 (sqrt (/ 1 y)))
(sqrt (/ 1 y))
(/ 1 y)
(+ (* (/ x (sqrt y)) 1/2) (sqrt y))
(/ x (sqrt y))
(sqrt y)
Outputs
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 y) #s(literal 0 binary64)))
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 y)) #s(literal -1/2 binary64)))
(fabs.f64 (sqrt.f64 y))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 y)))
(sqrt.f64 y)
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 y)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))
(/.f64 (sqrt.f64 y) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 y)))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 y)) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) y)) (sqrt.f64 #s(literal -1 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal -1/4 binary64))) (pow.f64 y #s(literal -1/4 binary64)))
(pow.f64 y #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 y) #s(literal 1 binary64))
(pow.f64 (*.f64 y y) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 y))
(*.f64 (sqrt.f64 y) #s(literal 1 binary64))
(*.f64 (sqrt.f64 y) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 y)))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 y)) #s(literal -1 binary64))
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64)))
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (*.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (/.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (sqrt.f64 y))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 y #s(literal -1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 y #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 y)) (sqrt.f64 (sqrt.f64 y)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 1/4 binary64))) (pow.f64 y #s(literal 1/4 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) y)))
(exp.f64 (fma.f64 #s(literal -1/2 binary64) (log.f64 y) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 y) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 y) #s(literal 0 binary64)) #s(literal -1 binary64)))
(fabs.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 y)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 y)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 y))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 y)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 y)) #s(literal -1 binary64))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (-.f64 #s(literal 0 binary64) y)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 0 binary64) y))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) y)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 0 binary64) y)))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) y))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 1/4 binary64))) (pow.f64 y #s(literal 1/4 binary64)))
(pow.f64 y #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 y) #s(literal -1 binary64))
(pow.f64 (*.f64 y y) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 y #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) y)) #s(literal 1/4 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 y)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 y)) #s(literal -1 binary64))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) y)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 0 binary64) y))))
(*.f64 (pow.f64 y #s(literal -1/4 binary64)) (pow.f64 y #s(literal -1/4 binary64)))
(*.f64 (pow.f64 y #s(literal -1/4 binary64)) (*.f64 (pow.f64 y #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 y #s(literal -1/4 binary64)) (/.f64 (pow.f64 y #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 y) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 y) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y))))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 y #s(literal -1/4 binary64))) (pow.f64 y #s(literal -1/4 binary64)))
(exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 y)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) y))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) y)))
(neg.f64 (/.f64 #s(literal -1 binary64) y))
(/.f64 #s(literal 1 binary64) y)
(/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (sqrt.f64 y))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) y))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 y)) (-.f64 #s(literal 0 binary64) (sqrt.f64 y)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (/.f64 #s(literal -1 binary64) (sqrt.f64 y))) #s(literal -1 binary64))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 y)) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) #s(literal -1 binary64))
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(*.f64 (+.f64 y (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 x x) y))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64)))))
(*.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y)) y) (-.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y)) y)) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) (sqrt.f64 y)))
(*.f64 (/.f64 (fma.f64 y (sqrt.f64 y) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 y (sqrt.f64 y)))) (fma.f64 (fma.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64)) y) (*.f64 y (*.f64 (+.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64))) (+.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64))))) (/.f64 (*.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 y (*.f64 y y))))) (fma.f64 (fma.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64)) y) (-.f64 (fma.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64)) y) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y))) (/.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 y y))))
(*.f64 (/.f64 (fma.f64 y (sqrt.f64 y) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 y (sqrt.f64 y)))) (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 y y)) (*.f64 y (*.f64 (+.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64))) (+.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64))))))) (-.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y)) (fma.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64)) y)))
(*.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y)) y) (-.f64 (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 y (sqrt.f64 y))) (*.f64 y (sqrt.f64 y)))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y) (fma.f64 (sqrt.f64 y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y)) y)))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 y) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (/.f64 x (sqrt.f64 y))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 y))) (neg.f64 (/.f64 x (sqrt.f64 y))))
(neg.f64 (neg.f64 (/.f64 x (sqrt.f64 y))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 y) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 y) x))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (/.f64 #s(literal 1 binary64) x))
(/.f64 x (sqrt.f64 y))
(/.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 y) x)))
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (sqrt.f64 y)))
(/.f64 (neg.f64 (/.f64 x (sqrt.f64 y))) #s(literal -1 binary64))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 y)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)) (sqrt.f64 y))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 y)))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 y)) x) #s(literal -1 binary64))
(/.f64 (/.f64 x #s(literal 1 binary64)) (sqrt.f64 y))
(/.f64 (/.f64 x #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 y)))
(/.f64 (/.f64 x (pow.f64 y #s(literal 1/4 binary64))) (pow.f64 y #s(literal 1/4 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)) (sqrt.f64 y))
(/.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) y)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (-.f64 #s(literal 0 binary64) y)))
(pow.f64 (/.f64 (sqrt.f64 y) x) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 y)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) x)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(*.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))
(*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (sqrt.f64 y))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 y)) (-.f64 #s(literal 0 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 y)))
(*.f64 (pow.f64 y #s(literal -1/4 binary64)) (*.f64 (pow.f64 y #s(literal -1/4 binary64)) x))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 y)))
(*.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 y)))
(*.f64 (/.f64 x (pow.f64 y #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 y) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 y) x) #s(literal -1/2 binary64)))
(*.f64 (*.f64 x (pow.f64 y #s(literal -1/4 binary64))) (pow.f64 y #s(literal -1/4 binary64)))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 y) #s(literal 0 binary64)))
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 y)) #s(literal -1/2 binary64)))
(fabs.f64 (sqrt.f64 y))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 y)))
(sqrt.f64 y)
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 y)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))
(/.f64 (sqrt.f64 y) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 y)))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 y)) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) y)) (sqrt.f64 #s(literal -1 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal -1/4 binary64))) (pow.f64 y #s(literal -1/4 binary64)))
(pow.f64 y #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 y) #s(literal 1 binary64))
(pow.f64 (*.f64 y y) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 y))
(*.f64 (sqrt.f64 y) #s(literal 1 binary64))
(*.f64 (sqrt.f64 y) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 y)))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 y)) #s(literal -1 binary64))
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64)))
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (*.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (/.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (sqrt.f64 y))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 y #s(literal -1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 y #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 y)) (sqrt.f64 (sqrt.f64 y)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 1/4 binary64))) (pow.f64 y #s(literal 1/4 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) y)))

simplify254.0ms (5.2%)

Memory
22.1MiB live, 293.3MiB allocated
Algorithm
egg-herbie
Rules
3 710×accelerator-lowering-fma.f32
3 710×accelerator-lowering-fma.f64
3 668×*-lowering-*.f32
3 668×*-lowering-*.f64
1 282×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
046570
1123558
2341554
3888554
41892554
54398554
65622554
76512554
87040554
97422554
107963554
08116536
Stop Event
iter limit
node limit
Counts
96 → 96
Calls
Call 1
Inputs
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(* -1 (sqrt y))
(* -1 (sqrt y))
(* -1 (sqrt y))
(* -1 (sqrt y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(sqrt y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(* 1/2 (* x (sqrt (/ 1 y))))
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
Outputs
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(* -1 (sqrt y))
(-.f64 #s(literal 0 binary64) (sqrt.f64 y))
(* -1 (sqrt y))
(-.f64 #s(literal 0 binary64) (sqrt.f64 y))
(* -1 (sqrt y))
(-.f64 #s(literal 0 binary64) (sqrt.f64 y))
(* -1 (sqrt y))
(-.f64 #s(literal 0 binary64) (sqrt.f64 y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y))
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y))
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y))
(* 1/2 (* x (sqrt (/ 1 y))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) #s(literal 0 binary64))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y))
(* 1/2 (* x (sqrt (/ 1 y))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) #s(literal 0 binary64))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y))
(* 1/2 (* x (sqrt (/ 1 y))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) #s(literal 0 binary64))
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/.f64 (fma.f64 (sqrt.f64 y) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/.f64 (fma.f64 (sqrt.f64 y) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/.f64 (fma.f64 (sqrt.f64 y) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) y)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) #s(literal 0 binary64))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) #s(literal 0 binary64))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) #s(literal 0 binary64))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) #s(literal 0 binary64))
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) #s(literal 0 binary64))
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(* x (sqrt (/ 1 y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64))
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)

eval46.0ms (0.9%)

Memory
14.8MiB live, 90.0MiB allocated
Compiler

Compiled 6 687 to 787 computations (88.2% saved)

prune43.0ms (0.9%)

Memory
-27.3MiB live, 91.3MiB allocated
Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New4380438
Fresh000
Picked022
Done033
Total4385443
Accuracy
100.0%
Counts
443 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.5%
(fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))
99.5%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y))))
96.7%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
100.0%
(sqrt.f64 (+.f64 x y))
97.1%
(sqrt.f64 y)
Compiler

Compiled 78 to 43 computations (44.9% saved)

regimes10.0ms (0.2%)

Memory
25.4MiB live, 25.4MiB allocated
Counts
6 → 1
Calls
Call 1
Inputs
(sqrt.f64 y)
(sqrt.f64 (+.f64 x y))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y))))
(fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y))
Outputs
(sqrt.f64 (+.f64 x y))
Calls

4 calls:

2.0ms
(+.f64 x y)
2.0ms
x
2.0ms
(sqrt.f64 (+.f64 x y))
2.0ms
y
Results
AccuracySegmentsBranch
100.0%1x
100.0%1y
100.0%1(sqrt.f64 (+.f64 x y))
100.0%1(+.f64 x y)
Compiler

Compiled 17 to 11 computations (35.3% saved)

regimes5.0ms (0.1%)

Memory
10.0MiB live, 10.0MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
(sqrt.f64 y)
Outputs
(sqrt.f64 y)
Calls

4 calls:

1.0ms
(sqrt.f64 (+.f64 x y))
1.0ms
(+.f64 x y)
1.0ms
x
1.0ms
y
Results
AccuracySegmentsBranch
97.1%1x
97.1%1y
97.1%1(sqrt.f64 (+.f64 x y))
97.1%1(+.f64 x y)
Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify39.0ms (0.8%)

Memory
-30.3MiB live, 8.6MiB allocated
Algorithm
egg-herbie
Rules
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
166
Stop Event
saturated
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 x y))
(sqrt.f64 y)
Outputs
(sqrt.f64 (+.f64 x y))
(sqrt.f64 y)

soundness188.0ms (3.8%)

Memory
-8.1MiB live, 77.0MiB allocated
Rules
28 536×accelerator-lowering-fma.f32
28 536×accelerator-lowering-fma.f64
5 638×*-lowering-*.f32
5 638×*-lowering-*.f64
2 832×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0156630
1454600
21425582
34619570
08274534
Stop Event
done
iter limit
node limit
Compiler

Compiled 12 to 8 computations (33.3% saved)

preprocess20.0ms (0.4%)

Memory
14.4MiB live, 53.5MiB allocated
Remove

(sort x y)

Compiler

Compiled 52 to 34 computations (34.6% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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