Details

Time bar (total: 1.3s)

analyze43.0ms (3.4%)

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
0%0%99.9%0.1%0%0%0%3
0%0%87.4%0.1%0%12.5%0%4
7.7%6.2%74.9%0.1%0%18.7%0%5
17.4%12.5%59.3%0.1%0%28.1%0%6
34.9%23.4%43.7%0.1%0%32.8%0%7
45.6%28.1%33.6%0.1%0%38.2%0%8
60.3%35.5%23.4%0.1%0%41%0%9
68.3%38.2%17.8%0.1%0%43.9%0%10
77.8%42.4%12.1%0.1%0%45.4%0%11
82.8%43.9%9.1%0.1%0%46.9%0%12
Compiler

Compiled 7 to 5 computations (28.6% saved)

sample909.0ms (70.8%)

Results
862.0ms8256×body256valid
35.0ms532×body256invalid
Bogosity

preprocess12.0ms (1%)

Algorithm
2×egg-herbie
Rules
2×swap-x-y
2×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0922
1922
022
122
Stop Event
1×unsound
1×saturated
Calls
Call 1
Inputs
0
1
Outputs
0
1
0
Call 2
Inputs
(sqrt.f64 (+.f64 x y))
(sqrt.f64 (+.f64 y x))
Outputs
(sqrt.f64 (+.f64 x y))
(sqrt.f64 (+.f64 y x))
(sqrt.f64 (+.f64 x y))
Symmetry

(sort x y)

Compiler

Compiled 8 to 6 computations (25% saved)

simplify39.0ms (3%)

Algorithm
1×egg-herbie
Rules
2×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
1811
Stop Event
1×saturated
Counts
1 → 1
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 x y))
Outputs
(sqrt.f64 (+.f64 x y))

eval0.0ms (0%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.01%
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.01%
(sqrt.f64 (+.f64 x y))
Compiler

Compiled 6 to 4 computations (33.3% saved)

localize5.0ms (0.4%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.01%
(sqrt.f64 (+.f64 x y))
Compiler

Compiled 11 to 4 computations (63.6% saved)

series2.0ms (0.2%)

Counts
1 → 8
Calls

6 calls:

TimeVariablePointExpression
0.0ms
x
@inf
(sqrt.f64 (+.f64 x y))
0.0ms
x
@0
(sqrt.f64 (+.f64 x y))
0.0ms
y
@0
(sqrt.f64 (+.f64 x y))
0.0ms
y
@inf
(sqrt.f64 (+.f64 x y))
0.0ms
x
@-inf
(sqrt.f64 (+.f64 x y))

rewrite53.0ms (4.1%)

Algorithm
1×batch-egg-rewrite
Rules
1552×add-sqr-sqrt
1534×*-un-lft-identity
1432×add-cube-cbrt
1418×add-cbrt-cube
1406×add-exp-log
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
114611
2191411
Stop Event
1×node limit
Counts
1 → 26
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 x y))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x y) 1/4) (pow.f64 (+.f64 x y) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 x y))) (cbrt.f64 (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 x y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (fma.f64 x x (*.f64 y (-.f64 y x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 y y))) (sqrt.f64 (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x y) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x y) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x y) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 y) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 x) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 x y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 x y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x y))))))))

simplify105.0ms (8.2%)

Algorithm
1×egg-herbie
Rules
1712×fma-def
1462×unswap-sqr
948×*-commutative
730×distribute-lft-in
634×associate-+r+
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01151096
1257960
2688844
31874804
44371804
Stop Event
1×node limit
Counts
34 → 72
Calls
Call 1
Inputs
(sqrt.f64 y)
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(+.f64 (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)))
(+.f64 (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (*.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3))) (sqrt.f64 y))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
(+.f64 (*.f64 -1/8 (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))))))
(+.f64 (*.f64 -1/8 (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (*.f64 1/16 (*.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x)))))))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 x y))) 1)
(*.f64 (sqrt.f64 (+.f64 x y)) 1)
(*.f64 1 (sqrt.f64 (+.f64 x y)))
(*.f64 (pow.f64 (+.f64 x y) 1/4) (pow.f64 (+.f64 x y) 1/4))
(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 x y))) (cbrt.f64 (+.f64 x y)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x y)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 x y)) 1/2))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (fma.f64 x x (*.f64 y (-.f64 y x)))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 y y))) (sqrt.f64 (-.f64 x y)))
(pow.f64 (+.f64 x y) 1/2)
(pow.f64 (sqrt.f64 (+.f64 x y)) 1)
(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x y))) 3)
(pow.f64 (pow.f64 (+.f64 x y) 3/2) 1/3)
(fabs.f64 (sqrt.f64 (+.f64 x y)))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 x y))))
(cbrt.f64 (pow.f64 (+.f64 x y) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x y))))
(hypot.f64 (sqrt.f64 y) (sqrt.f64 x))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 y))
(exp.f64 (log.f64 (sqrt.f64 (+.f64 x y))))
(exp.f64 (*.f64 (log.f64 (+.f64 x y)) 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 x y))) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x y))))
Outputs
(sqrt.f64 y)
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (sqrt.f64 y))
(+.f64 (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)))
(fma.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 x x)) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)))
(fma.f64 -1/8 (*.f64 x (*.f64 x (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)))
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 x (*.f64 x -1/8)) (sqrt.f64 y)))
(fma.f64 x (fma.f64 1/2 (sqrt.f64 (/.f64 1 y)) (*.f64 -1/8 (*.f64 x (sqrt.f64 (/.f64 1 (pow.f64 y 3)))))) (sqrt.f64 y))
(fma.f64 x (fma.f64 1/2 (sqrt.f64 (/.f64 1 y)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 x -1/8))) (sqrt.f64 y))
(+.f64 (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (*.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3))) (sqrt.f64 y))))
(fma.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 x x)) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)) (sqrt.f64 y))))
(fma.f64 -1/8 (*.f64 x (*.f64 x (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)) (sqrt.f64 y))))
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (fma.f64 -1/8 (*.f64 x (*.f64 x (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)) (sqrt.f64 y))))
(fma.f64 x (fma.f64 1/2 (sqrt.f64 (/.f64 1 y)) (*.f64 -1/8 (*.f64 x (sqrt.f64 (/.f64 1 (pow.f64 y 3)))))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (*.f64 1/16 (pow.f64 x 3)) (sqrt.f64 y)))
(fma.f64 x (fma.f64 1/2 (sqrt.f64 (/.f64 1 y)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 x -1/8))) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)) (sqrt.f64 y)))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
(+.f64 (sqrt.f64 x) (*.f64 (*.f64 1/2 y) (sqrt.f64 (/.f64 1 x))))
(fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))
(fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))
(+.f64 (*.f64 -1/8 (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))))))
(fma.f64 -1/8 (*.f64 (*.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (*.f64 (*.f64 1/2 y) (sqrt.f64 (/.f64 1 x)))))
(fma.f64 -1/8 (*.f64 y (*.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)))
(fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (fma.f64 -1/8 (*.f64 (*.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 x)))
(fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 y (*.f64 y -1/8)) (sqrt.f64 x)))
(+.f64 (*.f64 -1/8 (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (*.f64 1/16 (*.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x)))))))
(fma.f64 -1/8 (*.f64 (*.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (fma.f64 1/16 (*.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (sqrt.f64 x) (*.f64 (*.f64 1/2 y) (sqrt.f64 (/.f64 1 x))))))
(fma.f64 -1/8 (*.f64 y (*.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (fma.f64 1/16 (*.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))))
(fma.f64 (pow.f64 y 3) (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (fma.f64 -1/8 (*.f64 (*.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 x))))
(fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 (pow.f64 y 3) 1/16) (fma.f64 -1/8 (*.f64 (*.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 x))))
(fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (fma.f64 -1/8 (*.f64 (*.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 (pow.f64 y 3) 1/16) (sqrt.f64 x))))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 x y))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))
(*.f64 (sqrt.f64 (+.f64 x y)) 1)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))
(*.f64 1 (sqrt.f64 (+.f64 x y)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))
(*.f64 (pow.f64 (+.f64 x y) 1/4) (pow.f64 (+.f64 x y) 1/4))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))
(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))
(*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (sqrt.f64 (+.f64 y x))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 x y))) (cbrt.f64 (+.f64 x y)))
(*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (sqrt.f64 (+.f64 y x))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 y x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 y x))))
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 y x))) (sqrt.f64 (cbrt.f64 (+.f64 y x))))
(*.f64 (cbrt.f64 (+.f64 y x)) (sqrt.f64 (cbrt.f64 (+.f64 y x))))
(pow.f64 (cbrt.f64 (+.f64 y x)) 3/2)
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x y)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 x y)) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 y x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 y x))))
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 y x))) (sqrt.f64 (cbrt.f64 (+.f64 y x))))
(*.f64 (cbrt.f64 (+.f64 y x)) (sqrt.f64 (cbrt.f64 (+.f64 y x))))
(pow.f64 (cbrt.f64 (+.f64 y x)) 3/2)
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (fma.f64 x x (*.f64 y (-.f64 y x)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 y 3) (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x (*.f64 y (-.f64 y x)))))
(/.f64 (hypot.f64 (pow.f64 x 3/2) (pow.f64 y 3/2)) (sqrt.f64 (fma.f64 x x (*.f64 y (-.f64 y x)))))
(/.f64 (hypot.f64 (pow.f64 x 3/2) (pow.f64 y 3/2)) (sqrt.f64 (fma.f64 y (-.f64 y x) (*.f64 x x))))
(/.f64 (hypot.f64 (pow.f64 x 3/2) (pow.f64 y 3/2)) (sqrt.f64 (fma.f64 y y (*.f64 x (-.f64 x y)))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 y y))) (sqrt.f64 (-.f64 x y)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (sqrt.f64 (-.f64 x y)))
(pow.f64 (+.f64 x y) 1/2)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))
(pow.f64 (sqrt.f64 (+.f64 x y)) 1)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))
(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x y))) 3)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))
(pow.f64 (pow.f64 (+.f64 x y) 3/2) 1/3)
(cbrt.f64 (pow.f64 (+.f64 y x) 3/2))
(fabs.f64 (sqrt.f64 (+.f64 x y)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 x y))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))
(cbrt.f64 (pow.f64 (+.f64 x y) 3/2))
(cbrt.f64 (pow.f64 (+.f64 y x) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x y))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))
(hypot.f64 (sqrt.f64 y) (sqrt.f64 x))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 y))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))
(exp.f64 (log.f64 (sqrt.f64 (+.f64 x y))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))
(exp.f64 (*.f64 (log.f64 (+.f64 x y)) 1/2))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 x y))) 1))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x y))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 y x)) 1))
(+.f64 (sqrt.f64 (+.f64 y x)) 0)
(sqrt.f64 (+.f64 y x))

eval23.0ms (1.8%)

Compiler

Compiled 1099 to 663 computations (39.7% saved)

prune10.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New71172
Fresh000
Picked011
Done000
Total71273
Error
0%
Counts
73 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
✓0.01%
(sqrt.f64 (+.f64 x y))
▶1.6%
(sqrt.f64 y)
Compiler

Compiled 10 to 7 computations (30% saved)

localize4.0ms (0.3%)

Compiler

Compiled 5 to 3 computations (40% saved)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done011
Total022
Error
0%
Counts
2 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
✓0.01%
(sqrt.f64 (+.f64 x y))
✓1.6%
(sqrt.f64 y)
Compiler

Compiled 10 to 7 computations (30% saved)

regimes13.0ms (1%)

Accuracy

Total -1.0b remaining (-26180.3%)

Threshold costs -1b (-26180.3%)

Counts
2 → 1
Calls
Call 1
Inputs
(sqrt.f64 y)
(sqrt.f64 (+.f64 x y))
Outputs
(sqrt.f64 (+.f64 x y))
Calls

4 calls:

4.0ms
(sqrt.f64 (+.f64 x y))
3.0ms
(+.f64 x y)
3.0ms
y
3.0ms
x
Results
ErrorSegmentsBranch
0.01%1x
0.01%1y
0.01%1(sqrt.f64 (+.f64 x y))
0.01%1(+.f64 x y)
Compiler

Compiled 25 to 16 computations (36% saved)

simplify49.0ms (3.8%)

Algorithm
1×egg-herbie
Rules
2×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0816
1916
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 x y))
(sqrt.f64 y)
Outputs
(sqrt.f64 (+.f64 x y))
(sqrt.f64 y)
Compiler

Compiled 10 to 7 computations (30% saved)

soundness0.0ms (0%)

end15.0ms (1.1%)

Remove

(sort x y)

Compiler

Compiled 20 to 13 computations (35% saved)

Profiling

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