Details

Time bar (total: 1.4s)

analyze79.0ms (5.8%)

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)

sample1.0s (74.5%)

Results
841.0ms8256×body256valid
166.0ms516×body256invalid

preprocess36.0ms (2.6%)

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)

simplify14.0ms (1%)

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))

eval1.0ms (0%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0.1%)

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)

localize12.0ms (0.8%)

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)

series10.0ms (0.7%)

Counts
1 → 8
Calls

6 calls:

TimeVariablePointExpression
4.0ms
y
@0
(sqrt.f64 (+.f64 x y))
2.0ms
x
@inf
(sqrt.f64 (+.f64 x y))
2.0ms
x
@0
(sqrt.f64 (+.f64 x y))
1.0ms
x
@-inf
(sqrt.f64 (+.f64 x y))
1.0ms
y
@inf
(sqrt.f64 (+.f64 x y))

rewrite48.0ms (3.5%)

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))))))))

simplify89.0ms (6.5%)

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))))

eval9.0ms (0.7%)

Compiler

Compiled 473 to 281 computations (40.6% saved)

prune5.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New37138
Fresh000
Picked011
Done000
Total37239
Error
0.0b
Counts
39 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
✓0.0b
(sqrt.f64 (+.f64 x y))
▶1.8b
(sqrt.f64 y)
Compiler

Compiled 10 to 7 computations (30% saved)

localize3.0ms (0.2%)

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
0.0b
Counts
2 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
✓0.0b
(sqrt.f64 (+.f64 x y))
✓1.8b
(sqrt.f64 y)
Compiler

Compiled 10 to 7 computations (30% saved)

regimes23.0ms (1.7%)

Accuracy

Total -1.8b remaining (-45628.1%)

Threshold costs -1.8b (-45628.1%)

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
(+.f64 x y)
4.0ms
(sqrt.f64 (+.f64 x y))
3.0ms
y
3.0ms
x
Results
ErrorSegmentsBranch
0.0b1x
0.0b1y
0.0b1(sqrt.f64 (+.f64 x y))
0.0b1(+.f64 x y)
Compiler

Compiled 25 to 16 computations (36% saved)

simplify2.0ms (0.2%)

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%)

end16.0ms (1.2%)

Remove

(sort x y)

Compiler

Compiled 20 to 13 computations (35% saved)

Profiling

Loading profile data...