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

Time bar (total: 1.0s)

start0.0ms (0%)

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

analyze50.0ms (5%)

Memory
-30.6MiB live, 32.9MiB allocated; 37ms 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)

sample654.0ms (64.6%)

Memory
8.7MiB live, 791.5MiB allocated; 255ms collecting garbage
Samples
382.0ms8 256×0valid
14.0ms462×0invalid
Precisions
Click to see histograms. Total time spent on operations: 124.0ms
ival-sqrt: 94.0ms (75.8% of total)
ival-add!: 29.0ms (23.4% of total)
adjust: 1.0ms (0.8% of total)
Bogosity

preprocess14.0ms (1.3%)

Memory
23.4MiB live, 23.4MiB allocated; 0ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01430
12130
Stop Event
1×saturated
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 (0.6%)

Memory
8.1MiB live, 8.1MiB 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)

rewrite77.0ms (7.6%)

Memory
-7.0MiB live, 78.4MiB allocated; 23ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0188772
0189658
01062626
Stop Event
1×iter-limit
1×iter-limit
1×node-limit
1×iter-limit
Counts
33 → 37
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
(pow.f64 (+.f64 y x) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 y x))
(/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (-.f64 x y))
(/.f64 (fma.f64 (*.f64 x x) x (*.f64 (*.f64 y y) y)) (fma.f64 x x (-.f64 (*.f64 y y) (*.f64 x y))))
(+.f64 y x)
(+.f64 x y)
x
y
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) x) #s(literal 1/2 binary64) (sqrt.f64 y)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1/2 binary64))) x (sqrt.f64 y)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) #s(literal -1/8 binary64))) x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1/2 binary64))) x (sqrt.f64 y)))
#s(approx (+ x y) y)
#s(approx (+ x y) (+.f64 y x))
#s(approx x x)
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
#s(approx (sqrt (+ x y)) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (+ x y)) (*.f64 (+.f64 (fma.f64 (*.f64 (*.f64 y y) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (+ x y)) (*.f64 (+.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) (*.f64 y y) (fma.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) (*.f64 (*.f64 y y) y)) #s(literal 1/16 binary64) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (+ x y) (*.f64 (+.f64 (/.f64 y x) #s(literal 1 binary64)) x))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 x))))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64))) x)))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (*.f64 y y) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)))) x)))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (*.f64 y y) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (*.f64 (/.f64 (*.f64 (*.f64 y y) y) #s(literal 1 binary64)) (sqrt.f64 (pow.f64 x #s(literal -7 binary64)))) #s(literal 1/16 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64))))) x)))
#s(approx (+ x y) (neg.f64 (*.f64 (-.f64 (neg.f64 (/.f64 y x)) #s(literal 1 binary64)) x)))
#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y) #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y) #s(literal -1/8 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))) y (sqrt.f64 x)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) y) #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal -1/8 binary64))) y (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))) y (sqrt.f64 x)))
#s(approx (sqrt (+ x y)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (sqrt (+ x y)) (*.f64 (+.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (sqrt (+ x y)) (*.f64 (+.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (fma.f64 (*.f64 (sqrt.f64 (pow.f64 y #s(literal -7 binary64))) (*.f64 (*.f64 x x) x)) #s(literal 1/16 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 y))))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))) y)))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))))) y)))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) (sqrt.f64 (pow.f64 y #s(literal -5 binary64)))) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) x) #s(literal 1 binary64)) (sqrt.f64 (pow.f64 y #s(literal -7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))) y)))
#s(approx (+ x y) (neg.f64 (*.f64 (-.f64 (neg.f64 (/.f64 x y)) #s(literal 1 binary64)) y)))

eval4.0ms (0.4%)

Memory
7.8MiB live, 7.8MiB allocated; 0ms collecting garbage
Compiler

Compiled 399 to 178 computations (55.4% saved)

prune2.0ms (0.2%)

Memory
4.7MiB live, 4.7MiB allocated; 0ms collecting garbage
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New30434
Fresh000
Picked011
Done000
Total30535
Accuracy
100.0%
Counts
35 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(sqrt.f64 (+.f64 x y))
▶100.0%
(sqrt.f64 #s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)))
▶98.0%
(sqrt.f64 #s(approx (+ x y) y))
▶2.7%
#s(approx (sqrt (+ x y)) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
▶3.4%
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
Compiler

Compiled 40 to 40 computations (0% saved)

series29.0ms (2.8%)

Memory
-6.2MiB live, 46.8MiB allocated; 18ms collecting garbage
Counts
22 → 53
Calls
Call 1
Inputs
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
(sqrt.f64 x)
x
#s(approx (sqrt (+ x y)) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x)
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)))
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))
#s(literal 1 binary64)
(*.f64 (*.f64 x x) x)
(*.f64 x x)
y
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 #s(approx (+ x y) y))
#s(approx (+ x y) y)
(sqrt.f64 #s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)))
#s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y))
(*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)
(+.f64 (/.f64 x y) #s(literal 1 binary64))
(/.f64 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 (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* 1/2 (* (sqrt (/ 1 x)) y))))
#s(approx (* (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (/ (+ (sqrt (pow x 3)) (* 1/2 (* (sqrt x) y))) x)))
#s(approx (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
#s(approx (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (/ (+ (sqrt (pow x 3)) (* 1/2 (* (sqrt x) y))) (pow x 2))))
#s(approx (* (sqrt (/ 1 (* (* x x) x))) y) #s(hole binary64 (* (sqrt (/ 1 (pow x 3))) y)))
#s(approx (sqrt (/ 1 (* (* x x) x))) #s(hole binary64 (sqrt (/ 1 (pow x 3)))))
#s(approx (/ 1 (* (* x x) x)) #s(hole binary64 (/ 1 (pow x 3))))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ 1 (sqrt x)) #s(hole binary64 (sqrt (/ 1 x))))
#s(approx (+ x y) #s(hole binary64 y))
#s(approx (+ x y) #s(hole binary64 (+ x y)))
#s(approx (+ (/ x y) 1) #s(hole binary64 1))
#s(approx (+ (/ x y) 1) #s(hole binary64 (+ 1 (/ x 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 (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
#s(approx (+ x y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (+ (/ x y) 1) #s(hole binary64 (* x (+ (/ 1 x) (/ 1 y)))))
#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 (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))))))))
#s(approx (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))))))
#s(approx (* (sqrt (/ 1 (* (* x x) x))) y) #s(hole binary64 (* -1 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2))))))
#s(approx (sqrt (/ 1 (* (* x x) x))) #s(hole binary64 (* -1 (* (sqrt (/ 1 (pow x 3))) (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 (+ (/ x y) 1) #s(hole binary64 (/ (+ x y) 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 (* (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* y (+ (* 1/2 (sqrt (/ 1 x))) (* (sqrt x) (/ 1 y))))))
#s(approx (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (* y (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (/ 1 y))))))
#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 (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1 (* y (+ (* -1 (* (sqrt x) (/ 1 y))) (* -1/2 (sqrt (/ 1 x))))))))
#s(approx (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (* -1 (* y (+ (* -1 (* (sqrt (/ 1 x)) (/ 1 y))) (* -1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))
Calls

6 calls:

TimeVariablePointExpression
14.0ms
x
@-inf
((sqrt (+ x y)) (sqrt x) x (sqrt (+ x y)) (* (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) (* (sqrt (/ 1 (* (* x x) x))) y) (sqrt (/ 1 (* (* x x) x))) (/ 1 (* (* x x) x)) 1 (* (* x x) x) (* x x) y 1/2 (/ 1 (sqrt x)) (sqrt (+ x y)) (+ x y) (sqrt (+ x y)) (+ x y) (* (+ (/ x y) 1) y) (+ (/ x y) 1) (/ x y))
3.0ms
y
@0
((sqrt (+ x y)) (sqrt x) x (sqrt (+ x y)) (* (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) (* (sqrt (/ 1 (* (* x x) x))) y) (sqrt (/ 1 (* (* x x) x))) (/ 1 (* (* x x) x)) 1 (* (* x x) x) (* x x) y 1/2 (/ 1 (sqrt x)) (sqrt (+ x y)) (+ x y) (sqrt (+ x y)) (+ x y) (* (+ (/ x y) 1) y) (+ (/ x y) 1) (/ x y))
3.0ms
x
@0
((sqrt (+ x y)) (sqrt x) x (sqrt (+ x y)) (* (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) (* (sqrt (/ 1 (* (* x x) x))) y) (sqrt (/ 1 (* (* x x) x))) (/ 1 (* (* x x) x)) 1 (* (* x x) x) (* x x) y 1/2 (/ 1 (sqrt x)) (sqrt (+ x y)) (+ x y) (sqrt (+ x y)) (+ x y) (* (+ (/ x y) 1) y) (+ (/ x y) 1) (/ x y))
3.0ms
y
@-inf
((sqrt (+ x y)) (sqrt x) x (sqrt (+ x y)) (* (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) (* (sqrt (/ 1 (* (* x x) x))) y) (sqrt (/ 1 (* (* x x) x))) (/ 1 (* (* x x) x)) 1 (* (* x x) x) (* x x) y 1/2 (/ 1 (sqrt x)) (sqrt (+ x y)) (+ x y) (sqrt (+ x y)) (+ x y) (* (+ (/ x y) 1) y) (+ (/ x y) 1) (/ x y))
3.0ms
x
@inf
((sqrt (+ x y)) (sqrt x) x (sqrt (+ x y)) (* (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) (* (sqrt (/ 1 (* (* x x) x))) y) (sqrt (/ 1 (* (* x x) x))) (/ 1 (* (* x x) x)) 1 (* (* x x) x) (* x x) y 1/2 (/ 1 (sqrt x)) (sqrt (+ x y)) (+ x y) (sqrt (+ x y)) (+ x y) (* (+ (/ x y) 1) y) (+ (/ x y) 1) (/ x y))

rewrite65.0ms (6.4%)

Memory
-18.2MiB live, 70.0MiB allocated; 22ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02761468
03011213
014601174
Stop Event
1×iter-limit
1×iter-limit
1×node-limit
1×iter-limit
Counts
75 → 124
Calls
Call 1
Inputs
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
(sqrt.f64 x)
x
#s(approx (sqrt (+ x y)) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x)
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)))
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))
#s(literal 1 binary64)
(*.f64 (*.f64 x x) x)
(*.f64 x x)
y
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 #s(approx (+ x y) y))
#s(approx (+ x y) y)
(sqrt.f64 #s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)))
#s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y))
(*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)
(+.f64 (/.f64 x y) #s(literal 1 binary64))
(/.f64 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 (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* 1/2 (* (sqrt (/ 1 x)) y))))
#s(approx (* (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (/ (+ (sqrt (pow x 3)) (* 1/2 (* (sqrt x) y))) x)))
#s(approx (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
#s(approx (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (/ (+ (sqrt (pow x 3)) (* 1/2 (* (sqrt x) y))) (pow x 2))))
#s(approx (* (sqrt (/ 1 (* (* x x) x))) y) #s(hole binary64 (* (sqrt (/ 1 (pow x 3))) y)))
#s(approx (sqrt (/ 1 (* (* x x) x))) #s(hole binary64 (sqrt (/ 1 (pow x 3)))))
#s(approx (/ 1 (* (* x x) x)) #s(hole binary64 (/ 1 (pow x 3))))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ 1 (sqrt x)) #s(hole binary64 (sqrt (/ 1 x))))
#s(approx (+ x y) #s(hole binary64 y))
#s(approx (+ x y) #s(hole binary64 (+ x y)))
#s(approx (+ (/ x y) 1) #s(hole binary64 1))
#s(approx (+ (/ x y) 1) #s(hole binary64 (+ 1 (/ x 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 (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
#s(approx (+ x y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (+ (/ x y) 1) #s(hole binary64 (* x (+ (/ 1 x) (/ 1 y)))))
#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 (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))))))))
#s(approx (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))))))
#s(approx (* (sqrt (/ 1 (* (* x x) x))) y) #s(hole binary64 (* -1 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2))))))
#s(approx (sqrt (/ 1 (* (* x x) x))) #s(hole binary64 (* -1 (* (sqrt (/ 1 (pow x 3))) (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 (+ (/ x y) 1) #s(hole binary64 (/ (+ x y) 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 (* (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* y (+ (* 1/2 (sqrt (/ 1 x))) (* (sqrt x) (/ 1 y))))))
#s(approx (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (* y (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (/ 1 y))))))
#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 (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1 (* y (+ (* -1 (* (sqrt x) (/ 1 y))) (* -1/2 (sqrt (/ 1 x))))))))
#s(approx (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (* -1 (* y (+ (* -1 (* (sqrt (/ 1 x)) (/ 1 y))) (* -1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))
Outputs
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
x
#s(approx (sqrt (+ x y)) (*.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)) y (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
(*.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)) y (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x)
(*.f64 x (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)) y (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x (*.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)) x))
(fma.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64))))
(+.f64 (*.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (*.f64 x (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64))))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x) (*.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)) x))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (-.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (*.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)))) (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)) (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (*.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))))
(/.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 (*.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64))))))
(fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)) y (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) (*.f64 y #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y)))
(+.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y)
(*.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)))
(pow.f64 (*.f64 (*.f64 x x) x) #s(literal -1 binary64))
(pow.f64 x #s(literal -3 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (*.f64 x x) x)))
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))
#s(literal 1 binary64)
(*.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) (sqrt.f64 (*.f64 (*.f64 x x) x)))
(*.f64 (*.f64 x x) x)
(*.f64 x (*.f64 x x))
(pow.f64 x #s(literal 3 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
y
#s(literal 1/2 binary64)
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(pow.f64 #s(approx (+ x y) y) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (+ x y) y))
#s(approx (+ x y) y)
(pow.f64 #s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)))
#s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y))
(*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)
(*.f64 y (+.f64 (/.f64 x y) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) y (*.f64 (/.f64 x y) y))
(fma.f64 y #s(literal 1 binary64) (*.f64 y (/.f64 x y)))
(+.f64 (*.f64 y #s(literal 1 binary64)) (*.f64 y (/.f64 x y)))
(+.f64 (*.f64 #s(literal 1 binary64) y) (*.f64 (/.f64 x y) y))
(/.f64 (-.f64 (*.f64 (/.f64 x y) (/.f64 x y)) #s(literal 1 binary64)) (-.f64 (/.f64 x y) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 x y) (/.f64 x y))) (-.f64 #s(literal 1 binary64) (/.f64 x y)))
(/.f64 (+.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (/.f64 x y) (/.f64 x y) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 x y) #s(literal 1 binary64)))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (/.f64 x y) (/.f64 x y)) (*.f64 #s(literal 1 binary64) (/.f64 x y)))))
(+.f64 (/.f64 x y) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (/.f64 x y))
(/.f64 (neg.f64 x) (neg.f64 y))
(/.f64 x y)
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) x) #s(literal 1/2 binary64) (sqrt.f64 y)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1/2 binary64))) x (sqrt.f64 y)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) #s(literal -1/8 binary64))) x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1/2 binary64))) x (sqrt.f64 y)))
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx x x)
#s(approx (* (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y) #s(literal 1/2 binary64)))
#s(approx (* (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) y (sqrt.f64 (*.f64 (*.f64 x x) x))) x))
#s(approx (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)))
#s(approx (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) y (sqrt.f64 (*.f64 (*.f64 x x) x))) (*.f64 x x)))
#s(approx (* (sqrt (/ 1 (* (* x x) x))) y) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y))
#s(approx (sqrt (/ 1 (* (* x x) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))
#s(approx (/ 1 (* (* x x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)))
#s(approx (* (* x x) x) (*.f64 (*.f64 x x) x))
#s(approx (* x x) (*.f64 x x))
#s(approx (/ 1 (sqrt x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (+ x y) y)
#s(approx (+ x y) (+.f64 y x))
#s(approx (+ (/ x y) 1) #s(literal 1 binary64))
#s(approx (+ (/ x y) 1) (+.f64 (/.f64 x y) #s(literal 1 binary64)))
#s(approx (/ x y) (/.f64 x y))
#s(approx (sqrt (+ x y)) (*.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)) y (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (+ x y)) (*.f64 (+.f64 (fma.f64 (*.f64 (*.f64 y y) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (+ x y)) (*.f64 (+.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) (*.f64 y y) (fma.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) (*.f64 (*.f64 y y) y)) #s(literal 1/16 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)) y (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
#s(approx (+ x y) (*.f64 (+.f64 (/.f64 y x) #s(literal 1 binary64)) x))
#s(approx (+ (/ x y) 1) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) y)) x))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 x))))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)) y (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))) x)))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (*.f64 y y) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)) y (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))) x)))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (*.f64 y y) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (pow.f64 x #s(literal -7 binary64)))) (/.f64 (*.f64 (*.f64 y y) y) #s(literal 1 binary64)) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)) y (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))))) x)))
#s(approx (* (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) (neg.f64 (*.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1 binary64) y) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))) #s(literal 1/2 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))) x)))
#s(approx (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) (fma.f64 (*.f64 (*.f64 #s(literal -1 binary64) y) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
#s(approx (* (sqrt (/ 1 (* (* x x) x))) y) (neg.f64 (*.f64 (*.f64 #s(literal -1 binary64) y) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))))
#s(approx (sqrt (/ 1 (* (* x x) x))) (neg.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))))
#s(approx (+ x y) (neg.f64 (*.f64 (-.f64 (neg.f64 (/.f64 y x)) #s(literal 1 binary64)) x)))
#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y) #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) y) #s(literal -1/8 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))) y (sqrt.f64 x)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) y) #s(literal 1/16 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal -1/8 binary64))) y (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))) y (sqrt.f64 x)))
#s(approx (+ (/ x y) 1) (/.f64 (+.f64 y x) y))
#s(approx (sqrt (+ x y)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (sqrt (+ x y)) (*.f64 (+.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (sqrt (+ x y)) (*.f64 (+.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (fma.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) x)) (sqrt.f64 (pow.f64 y #s(literal -7 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (* (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) y))) y))
#s(approx (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) y))) y))
#s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 y))))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))) y)))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))))) y)))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) (sqrt.f64 (pow.f64 y #s(literal -5 binary64)))) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (sqrt.f64 (pow.f64 y #s(literal -7 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))) y)))
#s(approx (* (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) x) (neg.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (neg.f64 (*.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) y)))) y)))
#s(approx (+ (* (* (sqrt (/ 1 (* (* x x) x))) y) 1/2) (/ 1 (sqrt x))) (neg.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) (*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) y))) y)))
#s(approx (+ x y) (neg.f64 (*.f64 (-.f64 (neg.f64 (/.f64 x y)) #s(literal 1 binary64)) y)))

eval11.0ms (1.1%)

Memory
28.5MiB live, 28.5MiB allocated; 0ms collecting garbage
Compiler

Compiled 1 332 to 586 computations (56% saved)

prune5.0ms (0.4%)

Memory
12.3MiB live, 12.3MiB allocated; 0ms collecting garbage
Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New1070107
Fresh000
Picked044
Done011
Total1075112
Accuracy
100.0%
Counts
112 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(sqrt.f64 (+.f64 x y))
✓100.0%
(sqrt.f64 #s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)))
✓98.0%
(sqrt.f64 #s(approx (+ x y) y))
✓2.7%
#s(approx (sqrt (+ x y)) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
✓3.4%
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
Compiler

Compiled 71 to 66 computations (7% saved)

regimes12.0ms (1.2%)

Memory
-22.6MiB live, 22.8MiB allocated; 6ms collecting garbage
Counts
5 → 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))
(sqrt.f64 #s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)))
#s(approx (sqrt (+ x y)) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
Outputs
(sqrt.f64 #s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)))
Calls

4 calls:

5.0ms
y
2.0ms
x
2.0ms
(+.f64 x y)
2.0ms
(sqrt.f64 (+.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)

regimes7.0ms (0.7%)

Memory
15.8MiB live, 15.8MiB allocated; 0ms collecting garbage
Counts
3 → 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))
Outputs
(sqrt.f64 (+.f64 x y))
Calls

4 calls:

2.0ms
(sqrt.f64 (+.f64 x y))
2.0ms
y
2.0ms
(+.f64 x y)
2.0ms
x
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)

regimes31.0ms (3.1%)

Memory
-37.0MiB live, 20.4MiB allocated; 8ms 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:

25.0ms
(sqrt.f64 (+.f64 x y))
3.0ms
(+.f64 x y)
1.0ms
x
1.0ms
y
Results
AccuracySegmentsBranch
98.0%1(+.f64 x y)
98.0%1(sqrt.f64 (+.f64 x y))
98.0%1x
98.0%1y
Compiler

Compiled 9 to 11 computations (-22.2% saved)

regimes4.0ms (0.4%)

Memory
11.8MiB live, 11.8MiB 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
3.4%1x
3.4%1(+.f64 x y)
3.4%1(sqrt.f64 (+.f64 x y))
3.4%1y
Compiler

Compiled 9 to 11 computations (-22.2% saved)

derivations7.0ms (0.6%)

Memory
10.3MiB live, 10.3MiB allocated; 0ms collecting garbage
Stop Event
1×done
Compiler

Compiled 18 to 16 computations (11.1% saved)

preprocess35.0ms (3.5%)

Memory
-13.7MiB live, 77.6MiB allocated; 9ms collecting garbage
Remove

(sort x y)

Compiler

Compiled 70 to 68 computations (2.9% saved)

end0.0ms (0%)

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

Profiling

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