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

Time bar (total: 1.2s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze30.0ms (2.5%)

Memory
24.5MiB live, 70.1MiB allocated; 8ms collecting garbage
Algorithm
1×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)

sample843.0ms (70.1%)

Memory
-11.0MiB live, 669.4MiB allocated; 249ms collecting garbage
Samples
557.0ms8 256×0valid
27.0ms533×0invalid
Precisions
Click to see histograms. Total time spent on operations: 254.0ms
ival-sqrt: 138.0ms (54.3% of total)
ival-add!: 115.0ms (45.3% of total)
adjust: 1.0ms (0.4% of total)
Bogosity

preprocess88.0ms (7.3%)

Memory
-28.1MiB live, 29.3MiB allocated; 12ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01428
13124
25924
314824
439124
5124524
6584424
Stop Event
1×node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(sqrt.f64 (+.f64 x y))
Symmetry

(sort x y)

Compiler

Compiled 8 to 8 computations (0% saved)

series6.0ms (0.5%)

Memory
11.9MiB live, 11.9MiB allocated; 0ms collecting garbage
Counts
4 → 29
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 x y))
(+.f64 x y)
x
y
Outputs
#s(approx (sqrt (+ x y)) #s(hole binary64 (sqrt y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))))
#s(approx (+ x y) #s(hole binary64 y))
#s(approx (+ x y) #s(hole binary64 (+ x y)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ x y)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* 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))))))))
#s(approx (+ x y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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)))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* x (- (* -1 (/ y x)) 1)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* 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)))))))))))
#s(approx (+ x y) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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)))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))
Calls

6 calls:

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

rewrite34.0ms (2.9%)

Memory
4.9MiB live, 48.6MiB allocated; 7ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0188772
0189748
1517748
Stop Event
1×saturated
1×iter-limit
1×unsound
1×iter-limit
Counts
33 → 33
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 x y))
(+.f64 x y)
x
y
#s(approx (sqrt (+ x y)) #s(hole binary64 (sqrt y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))))
#s(approx (+ x y) #s(hole binary64 y))
#s(approx (+ x y) #s(hole binary64 (+ x y)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ x y)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* 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))))))))
#s(approx (+ x y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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)))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* x (- (* -1 (/ y x)) 1)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* 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)))))))))))
#s(approx (+ x y) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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)))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))
Outputs
(sqrt.f64 (+.f64 x y))
(+.f64 x y)
x
y
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 y) (*.f64 x (fma.f64 #s(literal -1/8 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 y) (*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))))))))))
#s(approx (+ x y) y)
#s(approx (+ x y) (+.f64 x y))
#s(approx x x)
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
#s(approx (sqrt (+ x y)) (*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y)))))
#s(approx (sqrt (+ x y)) (*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 y #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y))))))
#s(approx (sqrt (+ x y)) (*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 y #s(literal 2 binary64))) (fma.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y)))))))
#s(approx (+ x y) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x))))
#s(approx (sqrt (+ x y)) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))
#s(approx (sqrt (+ x y)) (*.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))))
#s(approx (sqrt (+ x y)) (*.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))))))
#s(approx (sqrt (+ x y)) (*.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 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 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))))))
#s(approx (+ x y) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 y x)) #s(literal 1 binary64)))))
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y))))
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 x) (*.f64 y (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 x) (*.f64 y (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 y (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) y))))))))
#s(approx (sqrt (+ x y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))))))))
#s(approx (sqrt (+ x y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))))))))))
#s(approx (sqrt (+ x y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))) (fma.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))))))))))
#s(approx (+ x y) (*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y))))
#s(approx (sqrt (+ x y)) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 y) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))
#s(approx (sqrt (+ x y)) (*.f64 #s(literal -1 binary64) (*.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))))
#s(approx (sqrt (+ x y)) (*.f64 #s(literal -1 binary64) (*.f64 y (fma.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))))))
#s(approx (sqrt (+ x y)) (*.f64 #s(literal -1 binary64) (*.f64 y (fma.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))) (fma.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 (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 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))))))
#s(approx (+ x y) (*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x y)) #s(literal 1 binary64)))))

eval3.0ms (0.2%)

Memory
5.3MiB live, 5.3MiB allocated; 0ms collecting garbage
Compiler

Compiled 410 to 183 computations (55.4% saved)

prune1.0ms (0.1%)

Memory
2.5MiB live, 2.5MiB allocated; 0ms collecting garbage
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New26329
Fresh000
Picked011
Done000
Total26430
Accuracy
100.0%
Counts
30 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(sqrt.f64 (+.f64 x y))
▶98.7%
(sqrt.f64 #s(approx (+ x y) y))
▶99.3%
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
▶3.1%
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
Compiler

Compiled 28 to 28 computations (0% saved)

series11.0ms (0.9%)

Memory
13.9MiB live, 13.9MiB allocated; 0ms collecting garbage
Counts
15 → 40
Calls
Call 1
Inputs
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
(sqrt.f64 x)
x
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(sqrt.f64 y)
y
(*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
#s(literal 1/2 binary64)
(*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal 1 binary64) y)
#s(literal 1 binary64)
(sqrt.f64 #s(approx (+ x y) y))
#s(approx (+ x y) y)
Outputs
#s(approx (sqrt (+ x y)) #s(hole binary64 (sqrt y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx x #s(hole binary64 x))
#s(approx (* 1/2 (* x (sqrt (/ 1 y)))) #s(hole binary64 (* 1/2 (* x (sqrt (/ 1 y))))))
#s(approx (* x (sqrt (/ 1 y))) #s(hole binary64 (* x (sqrt (/ 1 y)))))
#s(approx (+ x y) #s(hole binary64 y))
#s(approx (+ x y) #s(hole binary64 (+ x y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* 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))))))))
#s(approx (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) #s(hole binary64 (* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))))
#s(approx (+ x y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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)))))))))
#s(approx (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) #s(hole binary64 (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* x (- (* -1 (/ y x)) 1)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))))
#s(approx (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) #s(hole binary64 (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)))
#s(approx (sqrt (/ 1 y)) #s(hole binary64 (sqrt (/ 1 y))))
#s(approx (/ 1 y) #s(hole binary64 (/ 1 y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* 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)))))))))))
#s(approx (+ x y) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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)))))))))
#s(approx (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) #s(hole binary64 (* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (* 1/2 (* x (sqrt (/ 1 y)))) #s(hole binary64 (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))))
#s(approx (* x (sqrt (/ 1 y))) #s(hole binary64 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y)))))
#s(approx (sqrt (/ 1 y)) #s(hole binary64 (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))
Calls

6 calls:

TimeVariablePointExpression
3.0ms
y
@-inf
((sqrt (+ x y)) (sqrt x) x (sqrt (+ x y)) (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) (sqrt y) y (* 1/2 (* x (sqrt (/ 1 y)))) 1/2 (* x (sqrt (/ 1 y))) (sqrt (/ 1 y)) (/ 1 y) 1 (sqrt (+ x y)) (+ x y))
2.0ms
x
@-inf
((sqrt (+ x y)) (sqrt x) x (sqrt (+ x y)) (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) (sqrt y) y (* 1/2 (* x (sqrt (/ 1 y)))) 1/2 (* x (sqrt (/ 1 y))) (sqrt (/ 1 y)) (/ 1 y) 1 (sqrt (+ x y)) (+ x y))
2.0ms
x
@0
((sqrt (+ x y)) (sqrt x) x (sqrt (+ x y)) (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) (sqrt y) y (* 1/2 (* x (sqrt (/ 1 y)))) 1/2 (* x (sqrt (/ 1 y))) (sqrt (/ 1 y)) (/ 1 y) 1 (sqrt (+ x y)) (+ x y))
1.0ms
x
@inf
((sqrt (+ x y)) (sqrt x) x (sqrt (+ x y)) (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) (sqrt y) y (* 1/2 (* x (sqrt (/ 1 y)))) 1/2 (* x (sqrt (/ 1 y))) (sqrt (/ 1 y)) (/ 1 y) 1 (sqrt (+ x y)) (+ x y))
1.0ms
y
@0
((sqrt (+ x y)) (sqrt x) x (sqrt (+ x y)) (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) (sqrt y) y (* 1/2 (* x (sqrt (/ 1 y)))) 1/2 (* x (sqrt (/ 1 y))) (sqrt (/ 1 y)) (/ 1 y) 1 (sqrt (+ x y)) (+ x y))

rewrite52.0ms (4.3%)

Memory
-11.8MiB live, 31.1MiB allocated; 6ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02291059
02401032
16121032
Stop Event
1×saturated
1×iter-limit
1×unsound
1×iter-limit
Counts
55 → 55
Calls
Call 1
Inputs
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
(sqrt.f64 x)
x
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(sqrt.f64 y)
y
(*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
#s(literal 1/2 binary64)
(*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal 1 binary64) y)
#s(literal 1 binary64)
(sqrt.f64 #s(approx (+ x y) y))
#s(approx (+ x y) y)
#s(approx (sqrt (+ x y)) #s(hole binary64 (sqrt y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx x #s(hole binary64 x))
#s(approx (* 1/2 (* x (sqrt (/ 1 y)))) #s(hole binary64 (* 1/2 (* x (sqrt (/ 1 y))))))
#s(approx (* x (sqrt (/ 1 y))) #s(hole binary64 (* x (sqrt (/ 1 y)))))
#s(approx (+ x y) #s(hole binary64 y))
#s(approx (+ x y) #s(hole binary64 (+ x y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* 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))))))))
#s(approx (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) #s(hole binary64 (* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))))
#s(approx (+ x y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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)))))))))
#s(approx (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) #s(hole binary64 (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* x (- (* -1 (/ y x)) 1)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))))
#s(approx (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) #s(hole binary64 (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)))
#s(approx (sqrt (/ 1 y)) #s(hole binary64 (sqrt (/ 1 y))))
#s(approx (/ 1 y) #s(hole binary64 (/ 1 y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* 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)))))))))))
#s(approx (+ x y) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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)))))))))
#s(approx (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) #s(hole binary64 (* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (* 1/2 (* x (sqrt (/ 1 y)))) #s(hole binary64 (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))))
#s(approx (* x (sqrt (/ 1 y))) #s(hole binary64 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y)))))
#s(approx (sqrt (/ 1 y)) #s(hole binary64 (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))
Outputs
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
(sqrt.f64 x)
x
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(sqrt.f64 y)
y
(*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
#s(literal 1/2 binary64)
(*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal 1 binary64) y)
#s(literal 1 binary64)
(sqrt.f64 #s(approx (+ x y) y))
#s(approx (+ x y) y)
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 y) (*.f64 x (fma.f64 #s(literal -1/8 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 y) (*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))))))))))
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx x x)
#s(approx (* 1/2 (* x (sqrt (/ 1 y)))) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
#s(approx (* x (sqrt (/ 1 y))) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
#s(approx (+ x y) y)
#s(approx (+ x y) (+.f64 x y))
#s(approx (sqrt (+ x y)) (*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y)))))
#s(approx (sqrt (+ x y)) (*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 y #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y))))))
#s(approx (sqrt (+ x y)) (*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 y #s(literal 2 binary64))) (fma.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y)))))))
#s(approx (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) (*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 y)))))
#s(approx (+ x y) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x))))
#s(approx (sqrt (+ x y)) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))
#s(approx (sqrt (+ x y)) (*.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))))
#s(approx (sqrt (+ x y)) (*.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))))))
#s(approx (sqrt (+ x y)) (*.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 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 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))))))
#s(approx (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) (*.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 y)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))
#s(approx (+ x y) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 y x)) #s(literal 1 binary64)))))
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y))))
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 x) (*.f64 y (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 x) (*.f64 y (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 y (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) y))))))))
#s(approx (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) (/.f64 (+.f64 (sqrt.f64 (pow.f64 y #s(literal 3 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 y)))) y))
#s(approx (sqrt (/ 1 y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
#s(approx (/ 1 y) (/.f64 #s(literal 1 binary64) y))
#s(approx (sqrt (+ x y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))))))))
#s(approx (sqrt (+ x y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))))))))))
#s(approx (sqrt (+ x y)) (*.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))) (fma.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))))))))))
#s(approx (+ x y) (*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y))))
#s(approx (sqrt (+ x y)) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 y) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))
#s(approx (sqrt (+ x y)) (*.f64 #s(literal -1 binary64) (*.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))))
#s(approx (sqrt (+ x y)) (*.f64 #s(literal -1 binary64) (*.f64 y (fma.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))))))
#s(approx (sqrt (+ x y)) (*.f64 #s(literal -1 binary64) (*.f64 y (fma.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))) (fma.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 (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 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))))))
#s(approx (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) (*.f64 #s(literal -1 binary64) (*.f64 y (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))))
#s(approx (* 1/2 (* x (sqrt (/ 1 y)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
#s(approx (* x (sqrt (/ 1 y))) (*.f64 (*.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
#s(approx (sqrt (/ 1 y)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
#s(approx (+ x y) (*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x y)) #s(literal 1 binary64)))))

eval4.0ms (0.3%)

Memory
7.4MiB live, 7.4MiB allocated; 0ms collecting garbage
Compiler

Compiled 560 to 251 computations (55.2% saved)

prune2.0ms (0.2%)

Memory
4.6MiB live, 4.6MiB allocated; 0ms collecting garbage
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New39039
Fresh000
Picked033
Done011
Total39443
Accuracy
100.0%
Counts
43 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(sqrt.f64 (+.f64 x y))
✓98.7%
(sqrt.f64 #s(approx (+ x y) y))
✓99.3%
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
✓3.1%
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
Compiler

Compiled 50 to 47 computations (6% saved)

regimes7.0ms (0.6%)

Memory
13.8MiB live, 13.8MiB allocated; 0ms collecting garbage
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
(sqrt.f64 #s(approx (+ x y) y))
(sqrt.f64 (+.f64 x y))
#s(approx (sqrt (+ x y)) (+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
Outputs
(sqrt.f64 (+.f64 x y))
Calls

4 calls:

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

Compiled 9 to 11 computations (-22.2% saved)

regimes77.0ms (6.4%)

Memory
-34.0MiB live, 12.8MiB allocated; 3ms collecting garbage
Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
(sqrt.f64 #s(approx (+ x y) y))
Outputs
(sqrt.f64 #s(approx (+ x y) y))
Calls

4 calls:

72.0ms
y
2.0ms
x
1.0ms
(sqrt.f64 (+.f64 x y))
1.0ms
(+.f64 x y)
Results
AccuracySegmentsBranch
98.7%1(+.f64 x y)
98.7%1(sqrt.f64 (+.f64 x y))
98.7%1x
98.7%1y
Compiler

Compiled 9 to 11 computations (-22.2% saved)

regimes4.0ms (0.3%)

Memory
9.6MiB live, 9.6MiB allocated; 0ms collecting garbage
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

4 calls:

1.0ms
(sqrt.f64 (+.f64 x y))
1.0ms
y
1.0ms
(+.f64 x y)
1.0ms
x
Results
AccuracySegmentsBranch
3.1%1(+.f64 x y)
3.1%1(sqrt.f64 (+.f64 x y))
3.1%1x
3.1%1y
Compiler

Compiled 9 to 11 computations (-22.2% saved)

derivations2.0ms (0.1%)

Memory
2.0MiB live, 2.0MiB allocated; 0ms collecting garbage
Stop Event
1×done
Compiler

Compiled 11 to 10 computations (9.1% saved)

preprocess37.0ms (3.1%)

Memory
-14.8MiB live, 38.0MiB allocated; 13ms collecting garbage
Remove

(sort x y)

Compiler

Compiled 45 to 44 computations (2.2% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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