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

Time bar (total: 2.2s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze22.0ms (1%)

Memory
-0.1MiB live, 41.9MiB 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)

sample826.0ms (37.6%)

Memory
-144.1MiB live, 779.0MiB allocated
Samples
316.0ms8 256×0valid
21.0ms526×0invalid
Precisions
Click to see histograms. Total time spent on operations: 150.0ms
ival-add: 76.0ms (50.8% of total)
ival-sqrt: 63.0ms (42.1% of total)
ival-true: 7.0ms (4.7% of total)
ival-assert: 3.0ms (2% of total)
Bogosity

explain152.0ms (6.9%)

Memory
10.7MiB live, 88.4MiB 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
133.0ms512×0valid
Compiler

Compiled 26 to 16 computations (38.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-add: 5.0ms (51.1% of total)
ival-sqrt: 4.0ms (40.9% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess14.0ms (0.6%)

Memory
-5.1MiB live, 34.0MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01226
11526
044
064
174
074
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 x y))
Outputs
(sqrt.f64 (+.f64 x y))
(sqrt.f64 (+.f64 y x))
Symmetry

(sort x y)

Compiler

Compiled 4 to 4 computations (0% saved)

eval0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
1.6MiB live, 1.6MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(sqrt.f64 (+.f64 x y))
Compiler

Compiled 4 to 4 computations (0% saved)

simplify3.0ms (0.1%)

Memory
10.5MiB live, 10.5MiB allocated
Algorithm
egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 x y)
cost-diff0
(sqrt.f64 (+.f64 x y))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049
069
179
079
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 x y))
(+.f64 x y)
x
y
Outputs
(sqrt.f64 (+.f64 x y))
(sqrt.f64 (+.f64 y x))
(+.f64 x y)
(+.f64 y x)
x
y

localize16.0ms (0.7%)

Memory
-6.5MiB live, 36.7MiB allocated
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(+.f64 x y)
accuracy0.00390625
(sqrt.f64 (+.f64 x y))
Samples
12.0ms256×0valid
Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-sqrt: 3.0ms (67.8% of total)
ival-add: 1.0ms (22.6% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series5.0ms (0.2%)

Memory
11.1MiB live, 11.1MiB allocated
Counts
2 → 29
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 x y))
(+.f64 x y)
Outputs
(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))))))))))
y
(+ x y)
(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))))))
x
(* x (+ 1 (/ y x)))
(* -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)))))))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+ (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)))))))
(* 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)))))))))
(* y (+ 1 (/ x y)))
(* -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)))))))
(* -1 (* y (- (* -1 (/ x y)) 1)))
Calls

6 calls:

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

simplify212.0ms (9.6%)

Memory
-22.2MiB live, 181.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0156603
1496573
21984543
36459543
08257505
Stop Event
iter limit
node limit
Counts
29 → 27
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))))))))))
y
(+ x y)
(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))))))
x
(* x (+ 1 (/ y x)))
(* -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)))))))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+ (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)))))))
(* 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)))))))))
(* y (+ 1 (/ x y)))
(* -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)))))))
(* -1 (* y (- (* -1 (/ x y)) 1)))
Outputs
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) x (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 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) #s(literal -1/8 binary64))) x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) x (sqrt.f64 y))
y
(+ x y)
(+.f64 y x)
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(*.f64 (fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) y) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) 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 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64)) (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) y) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
x
(* x (+ 1 (/ y x)))
(fma.f64 (/.f64 y x) x 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 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) 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 (fma.f64 (*.f64 (*.f64 y y) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) y)) y (fma.f64 (*.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 y) x) #s(literal 1 binary64)))
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (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 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) 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 (fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/16 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) y)
(* y (+ 1 (/ x y)))
(fma.f64 (/.f64 x y) y 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 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) 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 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) 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 (fma.f64 (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 (neg.f64 y) (-.f64 (/.f64 (neg.f64 x) y) #s(literal 1 binary64)))

rewrite139.0ms (6.3%)

Memory
19.0MiB live, 172.4MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047
067
1227
21407
313597
089567
Stop Event
iter limit
node limit
iter limit
Counts
2 → 244
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 x y))
(+.f64 x y)
Outputs
(*.f64 (pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)))) (neg.f64 (neg.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)))))
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(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (*.f64 x x))) (-.f64 y x)) (/.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (*.f64 x x))) (-.f64 y x)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 y x)) (/.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 y x)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(-.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (*.f64 (neg.f64 (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(-.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (*.f64 (neg.f64 (*.f64 x x)) x) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(-.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (*.f64 (neg.f64 (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(-.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (*.f64 (neg.f64 (*.f64 x x)) x) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(-.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (*.f64 (neg.f64 (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 y #s(literal 3/2 binary64))) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (*.f64 (*.f64 (neg.f64 y) y) y) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (*.f64 (neg.f64 (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 y #s(literal 3/2 binary64))) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (*.f64 (*.f64 (neg.f64 y) y) y) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(-.f64 (*.f64 y (/.f64 y (-.f64 y x))) (*.f64 x (/.f64 x (-.f64 y x))))
(-.f64 (*.f64 x (/.f64 x (-.f64 y x))) (/.f64 (*.f64 (neg.f64 (neg.f64 y)) y) (-.f64 y x)))
(-.f64 (*.f64 x (/.f64 x (-.f64 y x))) (*.f64 y (/.f64 y (-.f64 y x))))
(-.f64 (neg.f64 y) x)
(-.f64 (neg.f64 x) y)
(-.f64 y (neg.f64 x))
(exp.f64 (log.f64 (+.f64 y x)))
(+.f64 (/.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (fma.f64 (-.f64 y x) y (*.f64 x x))) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))) (/.f64 (*.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (fma.f64 (-.f64 y x) y (*.f64 x x))) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(+.f64 (/.f64 (*.f64 y (fma.f64 (-.f64 y x) y (*.f64 x x))) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))) (/.f64 (*.f64 x (fma.f64 (-.f64 y x) y (*.f64 x x))) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(+.f64 (/.f64 (*.f64 x (fma.f64 (-.f64 y x) y (*.f64 x x))) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))) (/.f64 (*.f64 y (fma.f64 (-.f64 y x) y (*.f64 x x))) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(+.f64 (/.f64 (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x)))) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))) (/.f64 (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x)))) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(+.f64 (/.f64 (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) y) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))) (/.f64 (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) x) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(+.f64 (/.f64 (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) x) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))) (/.f64 (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) y) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(+.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (-.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))) (/.f64 (/.f64 (pow.f64 y #s(literal 9 binary64)) (-.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(+.f64 (/.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))))))) (/.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))))))))
(+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (pow.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) #s(literal 2 binary64))) (/.f64 (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) #s(literal 2 binary64))))
(+.f64 (/.f64 (pow.f64 y #s(literal 9 binary64)) (*.f64 (-.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64))) (fma.f64 (-.f64 y x) y (*.f64 x x)))) (/.f64 (pow.f64 x #s(literal 9 binary64)) (*.f64 (-.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64))) (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (*.f64 (-.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64))) (fma.f64 (-.f64 y x) y (*.f64 x x)))) (/.f64 (pow.f64 y #s(literal 9 binary64)) (*.f64 (-.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64))) (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(+.f64 (/.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (fma.f64 (-.f64 y x) y (*.f64 x x))) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (*.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (fma.f64 (-.f64 y x) y (*.f64 x x))) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(+.f64 (/.f64 (*.f64 y (fma.f64 (-.f64 y x) y (*.f64 x x))) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (*.f64 x (fma.f64 (-.f64 y x) y (*.f64 x x))) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(+.f64 (/.f64 (*.f64 x (fma.f64 (-.f64 y x) y (*.f64 x x))) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (*.f64 y (fma.f64 (-.f64 y x) y (*.f64 x x))) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(+.f64 (/.f64 (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x)))) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x)))) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(+.f64 (/.f64 (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) y) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) x) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(+.f64 (/.f64 (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) x) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) y) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(+.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (-.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64)))) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (/.f64 (pow.f64 y #s(literal 9 binary64)) (-.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64)))) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (fma.f64 y y (*.f64 x x)) (-.f64 y x))) (/.f64 (*.f64 (*.f64 (neg.f64 y) y) (*.f64 y y)) (*.f64 (fma.f64 y y (*.f64 x x)) (-.f64 y x))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 y x))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (*.f64 (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 y x))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 y x) y (*.f64 x x)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(+.f64 (cosh.f64 (log.f64 (+.f64 y x))) (sinh.f64 (log.f64 (+.f64 y x))))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(+.f64 (*.f64 y (/.f64 y (-.f64 y x))) (/.f64 (*.f64 (neg.f64 (neg.f64 x)) (neg.f64 x)) (-.f64 y x)))
(+.f64 (*.f64 y (/.f64 y (-.f64 y x))) (/.f64 (*.f64 (neg.f64 x) x) (-.f64 y x)))
(+.f64 (*.f64 y (/.f64 y (-.f64 y x))) (/.f64 (*.f64 x (neg.f64 x)) (-.f64 y x)))
(+.f64 (*.f64 y (/.f64 y (-.f64 y x))) (*.f64 x (/.f64 x (-.f64 y x))))
(+.f64 (*.f64 x (/.f64 x (-.f64 y x))) (/.f64 (*.f64 (neg.f64 (neg.f64 y)) (neg.f64 y)) (-.f64 y x)))
(+.f64 (*.f64 x (/.f64 x (-.f64 y x))) (*.f64 y (/.f64 y (-.f64 y x))))
(+.f64 y x)
(+.f64 x y)

eval32.0ms (1.5%)

Memory
-26.8MiB live, 49.1MiB allocated
Compiler

Compiled 6 896 to 897 computations (87% saved)

prune4.0ms (0.2%)

Memory
13.1MiB live, 13.1MiB allocated
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2672269
Fresh000
Picked011
Done000
Total2673270
Accuracy
100.0%
Counts
270 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(sqrt.f64 (+.f64 x y))
75.2%
(sqrt.f64 #s(approx (+ x y) (fma.f64 (/.f64 y x) x x)))
99.2%
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
Compiler

Compiled 22 to 17 computations (22.7% saved)

simplify134.0ms (6.1%)

Memory
-5.7MiB live, 77.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 y x)
cost-diff0
#s(approx (+ x y) (fma.f64 (/.f64 y x) x x))
cost-diff0
(sqrt.f64 #s(approx (+ x y) (fma.f64 (/.f64 y x) x x)))
cost-diff3
(fma.f64 (/.f64 y x) x x)
cost-diff0
(sqrt.f64 y)
cost-diff0
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01042
01542
12342
23739
36233
411833
528133
6129733
7216133
8247933
9266633
10268833
11268833
12328033
13359233
14375233
15376433
16376433
17376433
18392433
19405733
20405733
0803133
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
(sqrt.f64 y)
y
(sqrt.f64 #s(approx (+ x y) (fma.f64 (/.f64 y x) x x)))
#s(approx (+ x y) (fma.f64 (/.f64 y x) x x))
(fma.f64 (/.f64 y x) x x)
(/.f64 y x)
y
x
Outputs
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
(sqrt.f64 y)
y
(sqrt.f64 #s(approx (+ x y) (fma.f64 (/.f64 y x) x x)))
(sqrt.f64 #s(approx (+ x y) (+.f64 y x)))
#s(approx (+ x y) (fma.f64 (/.f64 y x) x x))
#s(approx (+ x y) (+.f64 y x))
(fma.f64 (/.f64 y x) x x)
(+.f64 y x)
(/.f64 y x)
y
x

localize25.0ms (1.2%)

Memory
-3.3MiB live, 34.2MiB allocated
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(/.f64 y x)
accuracy0.0
#s(approx (+ x y) (fma.f64 (/.f64 y x) x x))
accuracy0.00390625
(sqrt.f64 #s(approx (+ x y) (fma.f64 (/.f64 y x) x x)))
accuracy15.451910038439774
(fma.f64 (/.f64 y x) x x)
accuracy0.0
(sqrt.f64 y)
accuracy0.4928272593802774
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
Samples
19.0ms256×0valid
Compiler

Compiled 28 to 10 computations (64.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-sqrt: 6.0ms (48.4% of total)
ival-add: 3.0ms (24.2% of total)
ival-div: 2.0ms (16.1% of total)
ival-mult: 2.0ms (16.1% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series5.0ms (0.2%)

Memory
7.0MiB live, 7.0MiB allocated
Counts
6 → 30
Calls
Call 1
Inputs
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
(sqrt.f64 y)
(fma.f64 (/.f64 y x) x x)
(sqrt.f64 #s(approx (+ x y) (fma.f64 (/.f64 y x) x x)))
#s(approx (+ x y) (fma.f64 (/.f64 y x) x x))
(/.f64 y x)
Outputs
(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))))))))))
y
(+ x y)
(/ y x)
(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))))))
x
(* x (+ 1 (/ y x)))
(* -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)))))))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+ (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)))))))
(* 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)))))))))
(* y (+ 1 (/ x y)))
(* -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)))))))
(* -1 (* y (- (* -1 (/ x y)) 1)))
Calls

6 calls:

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

simplify184.0ms (8.4%)

Memory
8.9MiB live, 156.8MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0156606
1496576
21991546
36460546
08251508
Stop Event
iter limit
node limit
Counts
30 → 28
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))))))))))
y
(+ x y)
(/ y x)
(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))))))
x
(* x (+ 1 (/ y x)))
(* -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)))))))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+ (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)))))))
(* 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)))))))))
(* y (+ 1 (/ x y)))
(* -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)))))))
(* -1 (* y (- (* -1 (/ x y)) 1)))
Outputs
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) x (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 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) #s(literal -1/8 binary64))) x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) x (sqrt.f64 y))
y
(+ x y)
(+.f64 y x)
(/ y x)
(/.f64 y x)
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(*.f64 (fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) y) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) 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 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64)) (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) y) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
x
(* x (+ 1 (/ y x)))
(fma.f64 (/.f64 y x) x 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 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) 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 (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 y y) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) y)) y (fma.f64 (*.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 y) x) #s(literal 1 binary64)))
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (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 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) 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 (fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/16 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) y)
(* y (+ 1 (/ x y)))
(fma.f64 (/.f64 x y) y 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 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) 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 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) 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 (fma.f64 (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 (neg.f64 y) (-.f64 (/.f64 (neg.f64 x) y) #s(literal 1 binary64)))

rewrite189.0ms (8.6%)

Memory
5.3MiB live, 216.4MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01039
01539
15339
232836
3355136
0847033
Stop Event
iter limit
node limit
iter limit
Counts
6 → 189
Calls
Call 1
Inputs
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
(sqrt.f64 y)
(fma.f64 (/.f64 y x) x x)
(sqrt.f64 #s(approx (+ x y) (fma.f64 (/.f64 y x) x x)))
#s(approx (+ x y) (fma.f64 (/.f64 y x) x x))
(/.f64 y x)
Outputs
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
(*.f64 (pow.f64 (neg.f64 y) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 y) #s(literal 1/4 binary64)))
(*.f64 (neg.f64 (pow.f64 y #s(literal 1/4 binary64))) (neg.f64 (pow.f64 y #s(literal 1/4 binary64))))
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y))
(pow.f64 (neg.f64 (pow.f64 y #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1/4 binary64))
(pow.f64 (neg.f64 y) #s(literal 1/2 binary64))
(pow.f64 y #s(literal 1/2 binary64))
(sqrt.f64 y)
(fabs.f64 (sqrt.f64 y))
(exp.f64 (fma.f64 (log.f64 y) #s(literal 1/4 binary64) (*.f64 (log.f64 y) #s(literal 1/4 binary64))))
(exp.f64 (*.f64 (*.f64 (log.f64 y) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 y)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 y #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (sqrt.f64 y)))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 y))) (sinh.f64 (log.f64 (sqrt.f64 y))))
(*.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 (*.f64 y #s(literal -1 binary64)) #s(literal 4 binary64)) (pow.f64 (*.f64 (-.f64 x (*.f64 #s(literal 1 binary64) y)) x) #s(literal 2 binary64)))) (-.f64 (*.f64 #s(literal 1 binary64) (*.f64 y y)) (*.f64 (-.f64 x (*.f64 #s(literal 1 binary64) y)) x)))
(*.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 x (*.f64 #s(literal 1 binary64) y)) x) #s(literal 3 binary64)))) (fma.f64 (*.f64 (-.f64 x (*.f64 #s(literal 1 binary64) y)) x) (-.f64 (*.f64 (-.f64 x (*.f64 #s(literal 1 binary64) y)) x) (*.f64 #s(literal 1 binary64) (*.f64 y y))) (pow.f64 (*.f64 y #s(literal -1 binary64)) #s(literal 4 binary64))))
(*.f64 (/.f64 (fma.f64 (neg.f64 x) x (*.f64 #s(literal 1 binary64) (*.f64 y y))) (fma.f64 (neg.f64 x) x (*.f64 #s(literal 1 binary64) (*.f64 y y)))) (fma.f64 #s(literal 1 binary64) y x))
(*.f64 (/.f64 (fma.f64 (neg.f64 x) x (*.f64 #s(literal 1 binary64) (*.f64 y y))) (fma.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal 1 binary64) (*.f64 y y) (*.f64 x (fma.f64 #s(literal 1 binary64) y x))))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(*.f64 (*.f64 x (fma.f64 y (/.f64 y x) (-.f64 x (*.f64 #s(literal 1 binary64) y)))) (/.f64 (fma.f64 #s(literal 1 binary64) y x) (*.f64 x (fma.f64 y (/.f64 y x) (-.f64 x (*.f64 #s(literal 1 binary64) y))))))
(*.f64 (fma.f64 #s(literal 1 binary64) y x) (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) y) x) (-.f64 (*.f64 #s(literal 1 binary64) y) x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1 binary64)) x) (-.f64 (/.f64 y x) #s(literal 1 binary64)))
(/.f64 (*.f64 (+.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64)) x) (-.f64 (+.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 y x)))
(/.f64 (*.f64 x (-.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 (/.f64 y x) #s(literal 1 binary64)))
(/.f64 (*.f64 x (+.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 y x)))
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(fma.f64 y (pow.f64 (/.f64 x (neg.f64 x)) #s(literal 1 binary64)) x)
(fma.f64 y #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) x))
(fma.f64 y #s(literal 1 binary64) (*.f64 x #s(literal 1 binary64)))
(fma.f64 y #s(literal 1 binary64) x)
(fma.f64 x (sqrt.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64))) (*.f64 #s(literal 1 binary64) x))
(fma.f64 x (sqrt.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64))) (*.f64 x #s(literal 1 binary64)))
(fma.f64 x (sqrt.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64))) x)
(fma.f64 x (exp.f64 (log.f64 (/.f64 y x))) (*.f64 #s(literal 1 binary64) x))
(fma.f64 x (exp.f64 (log.f64 (/.f64 y x))) (*.f64 x #s(literal 1 binary64)))
(fma.f64 x (exp.f64 (log.f64 (/.f64 y x))) x)
(fma.f64 x (pow.f64 (/.f64 y x) #s(literal 1 binary64)) (*.f64 #s(literal 1 binary64) x))
(fma.f64 x (pow.f64 (/.f64 y x) #s(literal 1 binary64)) (*.f64 x #s(literal 1 binary64)))
(fma.f64 x (pow.f64 (/.f64 y x) #s(literal 1 binary64)) x)
(fma.f64 x (/.f64 (*.f64 x x) (*.f64 x (fma.f64 y (/.f64 y x) (-.f64 x (*.f64 #s(literal 1 binary64) y))))) (/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (*.f64 x (fma.f64 y (/.f64 y x) (-.f64 x (*.f64 #s(literal 1 binary64) y))))))
(fma.f64 x (/.f64 (*.f64 y (/.f64 y x)) (-.f64 (*.f64 #s(literal 1 binary64) y) x)) (*.f64 x (/.f64 x (-.f64 (*.f64 #s(literal 1 binary64) y) x))))
(fma.f64 x #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) y))
(fma.f64 x (/.f64 y x) (*.f64 #s(literal 1 binary64) x))
(fma.f64 x (/.f64 y x) (*.f64 x #s(literal 1 binary64)))
(fma.f64 x (/.f64 y x) x)
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (*.f64 #s(literal 1 binary64) y))) (/.f64 (*.f64 #s(literal 1 binary64) (*.f64 y y)) (-.f64 x (*.f64 #s(literal 1 binary64) y))))
(-.f64 (/.f64 (*.f64 #s(literal 1 binary64) (*.f64 y y)) (-.f64 (*.f64 #s(literal 1 binary64) y) x)) (*.f64 x (/.f64 x (-.f64 (*.f64 #s(literal 1 binary64) y) x))))
(-.f64 x (*.f64 y #s(literal -1 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 1 binary64) y))
(+.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 #s(literal 1 binary64) y))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 x (fma.f64 y (/.f64 y x) (-.f64 x (*.f64 #s(literal 1 binary64) y))))) (/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (*.f64 x (fma.f64 y (/.f64 y x) (-.f64 x (*.f64 #s(literal 1 binary64) y))))))
(+.f64 (/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (*.f64 x (fma.f64 y (/.f64 y x) (-.f64 x (*.f64 #s(literal 1 binary64) y))))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 x (fma.f64 y (/.f64 y x) (-.f64 x (*.f64 #s(literal 1 binary64) y))))))
(+.f64 (/.f64 (*.f64 #s(literal 1 binary64) (*.f64 y y)) (-.f64 (*.f64 #s(literal 1 binary64) y) x)) (*.f64 x (/.f64 x (-.f64 (*.f64 #s(literal 1 binary64) y) x))))
(+.f64 (*.f64 #s(literal 1 binary64) y) (*.f64 #s(literal 1 binary64) x))
(+.f64 (*.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) y) x)
(+.f64 x (*.f64 #s(literal 1 binary64) y))
(*.f64 (neg.f64 (pow.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x)) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x)) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x))))
(pow.f64 (neg.f64 (pow.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x)) #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x)))
(fabs.f64 (sqrt.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x))))
(exp.f64 (fma.f64 (log.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x))) #s(literal 1/4 binary64) (*.f64 (log.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x))) #s(literal 1/4 binary64))))
(exp.f64 (*.f64 (*.f64 (log.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (sqrt.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x)))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x))))) (sinh.f64 (log.f64 (sqrt.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x))))))
#s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x))
(exp.f64 (log.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x))))
(+.f64 (cosh.f64 (log.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x)))) (sinh.f64 (log.f64 #s(approx (+ x y) (fma.f64 #s(literal 1 binary64) y x)))))
(*.f64 #s(literal 1 binary64) (/.f64 y x))
(*.f64 (/.f64 y x) #s(literal 1 binary64))
(/.f64 (*.f64 y #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (neg.f64 y) (neg.f64 x))
(/.f64 (*.f64 #s(literal 1 binary64) y) x)
(/.f64 y x)
(neg.f64 (*.f64 (/.f64 (neg.f64 y) x) #s(literal 1 binary64)))
(neg.f64 (/.f64 (neg.f64 y) x))
(fabs.f64 (*.f64 (/.f64 (neg.f64 y) x) #s(literal 1 binary64)))
(fabs.f64 (/.f64 (neg.f64 y) x))
(fabs.f64 (/.f64 y x))

eval38.0ms (1.7%)

Memory
-6.5MiB live, 78.2MiB allocated
Compiler

Compiled 4 642 to 862 computations (81.4% saved)

prune4.0ms (0.2%)

Memory
10.8MiB live, 10.8MiB allocated
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New2140214
Fresh000
Picked022
Done011
Total2143217
Accuracy
100.0%
Counts
217 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(sqrt.f64 (+.f64 x y))
75.2%
(sqrt.f64 #s(approx (+ x y) (fma.f64 (/.f64 y x) x x)))
99.2%
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
Compiler

Compiled 44 to 29 computations (34.1% saved)

regimes8.0ms (0.3%)

Memory
-20.4MiB live, 18.8MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
(sqrt.f64 (+.f64 x y))
(sqrt.f64 #s(approx (+ x y) (fma.f64 (/.f64 y x) x x)))
Outputs
(sqrt.f64 (+.f64 x y))
Calls

4 calls:

3.0ms
(sqrt.f64 (+.f64 x y))
2.0ms
(+.f64 x y)
2.0ms
y
2.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
100.0%1y
100.0%1(sqrt.f64 (+.f64 x y))
100.0%1(+.f64 x y)
Compiler

Compiled 9 to 11 computations (-22.2% saved)

regimes4.0ms (0.2%)

Memory
11.3MiB live, 11.3MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
Outputs
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
Calls

4 calls:

1.0ms
(sqrt.f64 (+.f64 x y))
1.0ms
y
1.0ms
(+.f64 x y)
1.0ms
x
Results
AccuracySegmentsBranch
99.2%1x
99.2%1y
99.2%1(sqrt.f64 (+.f64 x y))
99.2%1(+.f64 x y)
Compiler

Compiled 9 to 11 computations (-22.2% saved)

simplify12.0ms (0.5%)

Memory
-22.5MiB live, 14.7MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
1911
Stop Event
saturated
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 x y))
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
Outputs
(sqrt.f64 (+.f64 x y))
#s(approx (sqrt (+ x y)) (sqrt.f64 y))

soundness154.0ms (7%)

Memory
3.9MiB live, 121.5MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0156603
1496573
21984543
36459543
08257505
Stop Event
done
iter limit
node limit
Compiler

Compiled 13 to 11 computations (15.4% saved)

preprocess16.0ms (0.7%)

Memory
35.1MiB live, 35.1MiB allocated
Remove

(sort x y)

Compiler

Compiled 46 to 40 computations (13% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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