Details

Time bar (total: 2.1s)

analyze50.0ms (2.4%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%87.4%12.6%4
6.2%74.9%18.8%5
12.5%59.3%28.2%6
23.4%43.7%32.9%7
28.1%33.6%38.3%8
35.5%23.4%41.1%9
38.2%17.8%44%10
42.4%12.1%45.5%11
43.9%9.1%47%12
Compiler

Compiled 7 to 5 computations (28.6% saved)

sample889.0ms (41.9%)

Results
834.0ms8256×body256valid
42.0ms492×body256invalid

preprocess17.0ms (0.8%)

Algorithm
2×egg-herbie
Rules
1×swap-x-y
1×+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
1712
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)

simplify6.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
1×+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
166
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
0.0b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.0b
(sqrt.f64 (+.f64 x y))
Compiler

Compiled 6 to 4 computations (33.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (+.f64 x y))
Compiler

Compiled 11 to 4 computations (63.6% saved)

series5.0ms (0.3%)

Counts
1 → 8
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(sqrt.f64 (+.f64 x y))
1.0ms
x
@0
(sqrt.f64 (+.f64 x y))
1.0ms
y
@inf
(sqrt.f64 (+.f64 x y))
1.0ms
y
@0
(sqrt.f64 (+.f64 x y))
1.0ms
x
@-inf
(sqrt.f64 (+.f64 x y))

rewrite49.0ms (2.3%)

Algorithm
1×batch-egg-rewrite
Rules
592×pow1_binary64
553×add-log-exp_binary64
553×log1p-expm1-u_binary64
553×expm1-log1p-u_binary64
539×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
11096
215076
Stop Event
1×node limit
Counts
1 → 24
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 (cbrt.f64 (sqrt.f64 (+.f64 x y))) (cbrt.f64 (+.f64 x y)))))) (#(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 (pow.f64 (+.f64 x y) 1/4) (pow.f64 (+.f64 x y) 1/4))))) (#(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 (*.f64 x x) (*.f64 y y))) (sqrt.f64 (-.f64 x y)))))) (#(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 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) 3/2) 1/3)))) (#(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) 1/4) 2)))) (#(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 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 expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 x y))))))))

simplify88.0ms (4.1%)

Algorithm
1×egg-herbie
Rules
679×fma-def_binary64
577×associate-+l+_binary64
544×associate-+r+_binary64
457×associate-*l*_binary64
388×distribute-rgt-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
051210
1130204
2339204
3959198
42937198
54374198
64938198
76701198
87725198
Stop Event
1×node limit
Counts
32 → 38
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)))))))
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))
(+.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 1/2 (*.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 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 x -1/8) (*.f64 1/2 (sqrt.f64 (/.f64 1 y)))) (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 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 x (*.f64 x -1/8)) (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 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 x -1/8) (*.f64 1/2 (sqrt.f64 (/.f64 1 y)))) (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)))))
(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 1/2 (*.f64 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 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 y (*.f64 y -1/8)) (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 -1/8 (*.f64 y y)) (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 1/2 (*.f64 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 -1/8 (*.f64 y (*.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (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) (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 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 y (*.f64 y -1/8)) (sqrt.f64 x))))
(fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (fma.f64 (pow.f64 y 3) (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 y (*.f64 y -1/8)) (sqrt.f64 x))))
(fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (fma.f64 (pow.f64 y 3) (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 -1/8 (*.f64 y y)) (sqrt.f64 x))))

eval17.0ms (0.8%)

Compiler

Compiled 473 to 281 computations (40.6% saved)

prune10.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New35338
Fresh000
Picked011
Done000
Total35439
Error
0b
Counts
39 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.5b
(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
▶1.5b
(sqrt.f64 y)
✓0.0b
(sqrt.f64 (+.f64 x y))
▶30.8b
(hypot.f64 (sqrt.f64 y) (sqrt.f64 x))
Compiler

Compiled 26 to 19 computations (26.9% saved)

localize5.0ms (0.2%)

Compiler

Compiled 5 to 3 computations (40% saved)

localize11.0ms (0.5%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(hypot.f64 (sqrt.f64 y) (sqrt.f64 x))
Compiler

Compiled 13 to 5 computations (61.5% saved)

series37.0ms (1.7%)

Counts
1 → 2
Calls

6 calls:

TimeVariablePointExpression
23.0ms
y
@inf
(hypot.f64 (sqrt.f64 y) (sqrt.f64 x))
4.0ms
y
@-inf
(hypot.f64 (sqrt.f64 y) (sqrt.f64 x))
3.0ms
x
@inf
(hypot.f64 (sqrt.f64 y) (sqrt.f64 x))
3.0ms
x
@-inf
(hypot.f64 (sqrt.f64 y) (sqrt.f64 x))
2.0ms
y
@0
(hypot.f64 (sqrt.f64 y) (sqrt.f64 x))

rewrite223.0ms (10.5%)

Algorithm
1×batch-egg-rewrite
Rules
497×pow1_binary64
471×add-sqr-sqrt_binary64
465×*-un-lft-identity_binary64
456×add-log-exp_binary64
456×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
066
11186
213206
Stop Event
1×node limit
Counts
1 → 17
Calls
Call 1
Inputs
(hypot.f64 (sqrt.f64 y) (sqrt.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 y x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 y x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 y x))) (cbrt.f64 (+.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (sqrt.f64 (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) (sqrt.f64 (sqrt.f64 (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 y x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (+.f64 y x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 y x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 y x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (+.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 y x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 y x))))))))

simplify10.0ms (0.4%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
Stop Event
1×saturated
Counts
19 → 19
Calls
Call 1
Inputs
(sqrt.f64 x)
(sqrt.f64 y)
Outputs
(sqrt.f64 x)
(sqrt.f64 y)

localize21.0ms (1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.5b
(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
Compiler

Compiled 21 to 11 computations (47.6% saved)

series19.0ms (0.9%)

Counts
1 → 24
Calls

6 calls:

TimeVariablePointExpression
4.0ms
x
@-inf
(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
3.0ms
y
@0
(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
3.0ms
y
@-inf
(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
3.0ms
x
@inf
(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
3.0ms
y
@inf
(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)

rewrite237.0ms (11.1%)

Algorithm
1×batch-egg-rewrite
Rules
801×pow1_binary64
752×add-log-exp_binary64
751×log1p-expm1-u_binary64
751×expm1-log1p-u_binary64
734×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
087
11826
221916
Stop Event
1×node limit
Counts
1 → 24
Calls
Call 1
Inputs
(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
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 (pow.f64 (+.f64 x y) 1/4) (pow.f64 (+.f64 x y) 1/4))))) (#(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 (cbrt.f64 (sqrt.f64 (+.f64 x y))) (cbrt.f64 (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 x y))) (*.f64 (cbrt.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 (pow.f64 (+.f64 x y) 1/8) (*.f64 (pow.f64 (+.f64 x y) 1/8) (pow.f64 (+.f64 x y) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 x y) 1/4) (pow.f64 (+.f64 x y) 1/8)) (pow.f64 (+.f64 x y) 1/8))))) (#(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 (*.f64 (pow.f64 (+.f64 x y) 1/4) (cbrt.f64 (sqrt.f64 (+.f64 x y)))) (cbrt.f64 (pow.f64 (+.f64 x y) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fma.f64 x x (neg.f64 (*.f64 y y)))) (sqrt.f64 (-.f64 x y)))))) (#(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 sqrt.f64 (+.f64 x y))))) (#(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 (sqrt.f64 (+.f64 x y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 x) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 y) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 x y))))))))

simplify106.0ms (5%)

Algorithm
1×egg-herbie
Rules
519×associate-+l+_binary64
449×associate-+r+_binary64
367×distribute-lft-in_binary64
367×distribute-rgt-in_binary64
252×unswap-sqr_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01851380
15751278
223351147
36744931
Stop Event
1×node limit
Counts
48 → 62
Calls
Call 1
Inputs
(sqrt.f64 y)
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (sqrt.f64 y) (*.f64 (+.f64 (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) (pow.f64 x 2))))
(+.f64 (*.f64 (+.f64 (*.f64 -3/64 (sqrt.f64 (/.f64 1 (pow.f64 y 5)))) (*.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))))) (pow.f64 x 3)) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (sqrt.f64 y) (*.f64 (+.f64 (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) (pow.f64 x 2)))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
(+.f64 (*.f64 1/16 (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1/8 (pow.f64 y 2)) (*.f64 1/32 (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 1/2 (*.f64 (*.f64 y (+.f64 (*.f64 -1/8 (pow.f64 y 2)) (*.f64 1/32 (pow.f64 y 2)))) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (*.f64 1/16 (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1/8 (pow.f64 y 2)) (*.f64 1/32 (pow.f64 y 2))) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 1/384 (pow.f64 y 3)) (+.f64 (*.f64 1/12 (pow.f64 y 3)) (*.f64 -1/32 (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)))))))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (*.f64 1/2 (/.f64 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) y) x)))
(+.f64 (*.f64 2 (/.f64 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (*.f64 -1/8 (pow.f64 y 2)) (*.f64 1/32 (pow.f64 y 2)))) (pow.f64 x 2))) (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) y) x)) (*.f64 1/16 (/.f64 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 y 2)) (pow.f64 x 2))))))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (*.f64 y (+.f64 (*.f64 -1/8 (pow.f64 y 2)) (*.f64 1/32 (pow.f64 y 2)))))) (*.f64 2 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (*.f64 1/32 (pow.f64 y 3)) (+.f64 (*.f64 -1/384 (pow.f64 y 3)) (*.f64 -1/12 (pow.f64 y 3))))))) (pow.f64 x 3))) (+.f64 (*.f64 2 (/.f64 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (*.f64 -1/8 (pow.f64 y 2)) (*.f64 1/32 (pow.f64 y 2)))) (pow.f64 x 2))) (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) y) x)) (*.f64 1/16 (/.f64 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 y 2)) (pow.f64 x 2)))))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
(+.f64 (*.f64 (pow.f64 y 2) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))))))
(+.f64 (*.f64 (pow.f64 y 3) (+.f64 (*.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (*.f64 -3/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))) (+.f64 (*.f64 (pow.f64 y 2) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x)))))))
(sqrt.f64 y)
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (*.f64 2 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/32 (pow.f64 x 2))))) (+.f64 (*.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))) (sqrt.f64 y))))
(+.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 1/12 (pow.f64 x 3)) (+.f64 (*.f64 1/384 (pow.f64 x 3)) (*.f64 -1/32 (pow.f64 x 3)))) (sqrt.f64 (/.f64 1 (pow.f64 y 5))))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (*.f64 (+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/32 (pow.f64 x 2))) x))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (*.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))) (+.f64 (*.f64 2 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/32 (pow.f64 x 2))))) (sqrt.f64 y))))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2)
(+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) (*.f64 1/2 (/.f64 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) x) y)))
(+.f64 (*.f64 2 (/.f64 (*.f64 (+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/32 (pow.f64 x 2))) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2)) (pow.f64 y 2))) (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) (+.f64 (*.f64 1/16 (/.f64 (*.f64 (pow.f64 x 2) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2)) (pow.f64 y 2))) (*.f64 1/2 (/.f64 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) x) y)))))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 1/32 (pow.f64 x 3)) (+.f64 (*.f64 -1/384 (pow.f64 x 3)) (*.f64 -1/12 (pow.f64 x 3)))) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2))) (*.f64 -1/2 (*.f64 (+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/32 (pow.f64 x 2))) (*.f64 x (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2))))) (pow.f64 y 3))) (+.f64 (*.f64 2 (/.f64 (*.f64 (+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/32 (pow.f64 x 2))) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2)) (pow.f64 y 2))) (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) (+.f64 (*.f64 1/16 (/.f64 (*.f64 (pow.f64 x 2) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2)) (pow.f64 y 2))) (*.f64 1/2 (/.f64 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) 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 (*.f64 1/2 (sqrt.f64 (/.f64 1 y))) x (sqrt.f64 y))
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (sqrt.f64 y) (*.f64 (+.f64 (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) (pow.f64 x 2))))
(+.f64 (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8) (*.f64 x x)))
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (fma.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8) (*.f64 x x) (sqrt.f64 y)))
(+.f64 (*.f64 (+.f64 (*.f64 -3/64 (sqrt.f64 (/.f64 1 (pow.f64 y 5)))) (*.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))))) (pow.f64 x 3)) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (sqrt.f64 y) (*.f64 (+.f64 (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) (pow.f64 x 2)))))
(fma.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) 1/16) (pow.f64 x 3) (+.f64 (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8) (*.f64 x x))))
(fma.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 5)))) (pow.f64 x 3) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (fma.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8) (*.f64 x x) (sqrt.f64 y))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
(fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))
(+.f64 (*.f64 1/16 (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1/8 (pow.f64 y 2)) (*.f64 1/32 (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 1/16 (*.f64 (*.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (fma.f64 2 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (*.f64 y y) -3/32)) (+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x)))))))
(+.f64 (fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/16 (*.f64 y y)) (*.f64 2 (*.f64 y (*.f64 y -3/32))))))
(+.f64 (fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 (*.f64 1/16 y) y) (*.f64 2 (*.f64 y (*.f64 y -3/32))))))
(+.f64 (*.f64 1/2 (*.f64 (*.f64 y (+.f64 (*.f64 -1/8 (pow.f64 y 2)) (*.f64 1/32 (pow.f64 y 2)))) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (*.f64 1/16 (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1/8 (pow.f64 y 2)) (*.f64 1/32 (pow.f64 y 2))) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 1/384 (pow.f64 y 3)) (+.f64 (*.f64 1/12 (pow.f64 y 3)) (*.f64 -1/32 (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 1/2 (*.f64 (*.f64 y (*.f64 (*.f64 y y) -3/32)) (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (fma.f64 1/16 (*.f64 (*.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (fma.f64 2 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (*.f64 y y) -3/32)) (fma.f64 2 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 1/384 (pow.f64 y 3) (*.f64 (pow.f64 y 3) 5/96))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x)))))))))
(fma.f64 1/2 (*.f64 (*.f64 (pow.f64 y 3) -3/32) (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (fma.f64 2 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 (pow.f64 y 3) 7/128)) (fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/16 (*.f64 y y)) (*.f64 2 (*.f64 y (*.f64 y -3/32)))))))
(fma.f64 1/2 (*.f64 (*.f64 (pow.f64 y 3) -3/32) (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (fma.f64 2 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 (pow.f64 y 3) 7/128)) (fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 (*.f64 1/16 y) y) (*.f64 2 (*.f64 y (*.f64 y -3/32)))))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)
(pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 x) -1/4)) 2)
(sqrt.f64 (exp.f64 (log.f64 x)))
(+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (*.f64 1/2 (/.f64 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) y) x)))
(+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (*.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (/.f64 x y))))
(fma.f64 1/2 (*.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) y) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))
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(fma.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 x y) (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 y) -1/4)) 2)) (/.f64 x y)) -3/32) (+.f64 (fma.f64 1/2 (*.f64 (/.f64 x y) (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 y) -1/4)) 2)) (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 y) -1/4)) 2)) (*.f64 (/.f64 (*.f64 1/16 (*.f64 x x)) y) (/.f64 (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 y) -1/4)) 2) y))))
(fma.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 x y) (sqrt.f64 (exp.f64 (log.f64 y)))) (/.f64 x y)) -3/32) (+.f64 (fma.f64 1/2 (*.f64 (/.f64 x y) (sqrt.f64 (exp.f64 (log.f64 y)))) (sqrt.f64 (exp.f64 (log.f64 y)))) (*.f64 (/.f64 (*.f64 1/16 (*.f64 x x)) y) (/.f64 (sqrt.f64 (exp.f64 (log.f64 y))) y))))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 1/32 (pow.f64 x 3)) (+.f64 (*.f64 -1/384 (pow.f64 x 3)) (*.f64 -1/12 (pow.f64 x 3)))) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2))) (*.f64 -1/2 (*.f64 (+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/32 (pow.f64 x 2))) (*.f64 x (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2))))) (pow.f64 y 3))) (+.f64 (*.f64 2 (/.f64 (*.f64 (+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/32 (pow.f64 x 2))) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2)) (pow.f64 y 2))) (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) (+.f64 (*.f64 1/16 (/.f64 (*.f64 (pow.f64 x 2) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2)) (pow.f64 y 2))) (*.f64 1/2 (/.f64 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) x) y))))))
(fma.f64 -1 (/.f64 (fma.f64 2 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2) (fma.f64 1/32 (pow.f64 x 3) (*.f64 (pow.f64 x 3) -11/128))) (*.f64 -1/2 (*.f64 (*.f64 (*.f64 x x) -3/32) (*.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2))))) (pow.f64 y 3)) (fma.f64 2 (/.f64 (*.f64 (*.f64 x x) -3/32) (/.f64 (*.f64 y y) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2))) (+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2) (fma.f64 1/16 (/.f64 (*.f64 x x) (/.f64 (*.f64 y y) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2))) (*.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2) (/.f64 y x)))))))
(-.f64 (+.f64 (fma.f64 1/2 (/.f64 x (/.f64 y (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2))) (/.f64 (*.f64 (*.f64 x x) 1/16) (/.f64 (*.f64 y y) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2)))) (fma.f64 2 (*.f64 (/.f64 (*.f64 x (*.f64 x -3/32)) y) (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2) y)) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2))) (/.f64 (fma.f64 2 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2) (*.f64 (pow.f64 x 3) -7/128)) (*.f64 -1/2 (*.f64 (*.f64 (pow.f64 x 3) -3/32) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2)))) (pow.f64 y 3)))
(-.f64 (fma.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 x y) (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 y) -1/4)) 2)) (/.f64 x y)) -3/32) (+.f64 (fma.f64 1/2 (*.f64 (/.f64 x y) (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 y) -1/4)) 2)) (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 y) -1/4)) 2)) (*.f64 (/.f64 (*.f64 1/16 (*.f64 x x)) y) (/.f64 (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 y) -1/4)) 2) y)))) (/.f64 (*.f64 (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 y) -1/4)) 2) (+.f64 (*.f64 2 (*.f64 (pow.f64 x 3) -7/128)) (*.f64 -1/2 (*.f64 (pow.f64 x 3) -3/32)))) (pow.f64 y 3)))
(-.f64 (fma.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 x y) (sqrt.f64 (exp.f64 (log.f64 y)))) (/.f64 x y)) -3/32) (+.f64 (fma.f64 1/2 (*.f64 (/.f64 x y) (sqrt.f64 (exp.f64 (log.f64 y)))) (sqrt.f64 (exp.f64 (log.f64 y)))) (*.f64 (/.f64 (*.f64 1/16 (*.f64 x x)) y) (/.f64 (sqrt.f64 (exp.f64 (log.f64 y))) y)))) (/.f64 (*.f64 (sqrt.f64 (exp.f64 (log.f64 y))) (+.f64 (*.f64 2 (*.f64 (pow.f64 x 3) -7/128)) (*.f64 -1/2 (*.f64 (pow.f64 x 3) -3/32)))) (pow.f64 y 3)))

eval82.0ms (3.9%)

Compiler

Compiled 2032 to 1380 computations (32.1% saved)

prune13.0ms (0.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New81081
Fresh000
Picked011
Done033
Total81485
Error
0b
Counts
85 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
✓0.5b
(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
✓1.5b
(sqrt.f64 y)
✓0.0b
(sqrt.f64 (+.f64 x y))
✓30.8b
(hypot.f64 (sqrt.f64 y) (sqrt.f64 x))
Compiler

Compiled 26 to 19 computations (26.9% saved)

regimes19.0ms (0.9%)

Accuracy

Total -31.9b remaining (-407816.4%)

Threshold costs -31.9b (-407816.4%)

Counts
4 → 1
Calls
Call 1
Inputs
(sqrt.f64 y)
(sqrt.f64 (+.f64 x y))
(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
(hypot.f64 (sqrt.f64 y) (sqrt.f64 x))
Outputs
(sqrt.f64 (+.f64 x y))
Calls

4 calls:

5.0ms
y
4.0ms
(sqrt.f64 (+.f64 x y))
4.0ms
(+.f64 x y)
4.0ms
x
Results
ErrorSegmentsBranch
0.0b1x
0.0b1y
0.0b1(sqrt.f64 (+.f64 x y))
0.0b1(+.f64 x y)
Compiler

Compiled 37 to 22 computations (40.5% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
1×+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
179
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%)

end202.0ms (9.5%)

Remove

(sort x y)

Compiler

Compiled 20 to 13 computations (35% saved)

Profiling

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