Details

Time bar (total: 1.2s)

analyze40.0ms (3.5%)

Algorithm
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%99.9%0.1%4
25%74.9%0.1%5
25%50%25.1%6
25%31.2%43.8%7
31.2%25%43.8%8
39%17.2%43.8%9
42.9%13.3%43.8%10
47.2%9%43.8%11
49.4%6.8%43.8%12
Compiler

Compiled 10 to 6 computations (40% saved)

sample735.0ms (63.8%)

Results
723.0ms8256×body256valid
0.0msbody256invalid

preprocess20.0ms (1.7%)

Algorithm
egg-herbie
Rules
fma-def_binary64
swap-x-y
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0716
1916
022
122
Stop Event
unsound
saturated
Calls
Call 1
Inputs
0
1
Outputs
0
1
0
Call 2
Inputs
(+.f64 (*.f64 x x) (*.f64 y y))
(+.f64 (*.f64 y y) (*.f64 x x))
Outputs
(+.f64 (*.f64 x x) (*.f64 y y))
(fma.f64 x x (*.f64 y y))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 x x (*.f64 y y))
Symmetry

(sort x y)

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify11.0ms (0.9%)

Algorithm
egg-herbie
Rules
fma-def_binary64
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
298
Stop Event
saturated
Counts
1 → 2
Calls
Call 1
Inputs
(+.f64 (*.f64 x x) (*.f64 y y))
Outputs
(+.f64 (*.f64 x x) (*.f64 y y))
(fma.f64 x x (*.f64 y y))

eval0.0ms (0%)

Compiler

Compiled 15 to 6 computations (60% saved)

prune1.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0b
Counts
3 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
0b
(fma.f64 x x (*.f64 y y))
0.0b
(+.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 17 to 9 computations (47.1% saved)

localize4.0ms (0.4%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 x x) (*.f64 y y))
0.0b
(+.f64 (*.f64 x x) (*.f64 y y))

series3.0ms (0.3%)

Counts
1 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@0
(+.f64 (*.f64 x x) (*.f64 y y))
1.0ms
y
@0
(+.f64 (*.f64 x x) (*.f64 y y))
1.0ms
x
@inf
(+.f64 (*.f64 x x) (*.f64 y y))
0.0ms
y
@inf
(+.f64 (*.f64 x x) (*.f64 y y))
0.0ms
y
@-inf
(+.f64 (*.f64 x x) (*.f64 y y))

rewrite50.0ms (4.4%)

Algorithm
batch-egg-rewrite
Rules
650×pow1_binary64
606×add-log-exp_binary64
606×log1p-expm1-u_binary64
606×expm1-log1p-u_binary64
589×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
068
11297
217487
Stop Event
node limit
Counts
1 → 33
Calls
Call 1
Inputs
(+.f64 (*.f64 x x) (*.f64 y y))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (hypot.f64 x y) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 4) (-.f64 (*.f64 x x) (*.f64 y y))) (/.f64 (pow.f64 y 4) (-.f64 (*.f64 x x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 x y) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (hypot.f64 x y) 2)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x y) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x y) 2)) 2) (cbrt.f64 (pow.f64 (hypot.f64 x y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x y) (hypot.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 6)) (/.f64 1 (+.f64 (pow.f64 x 4) (-.f64 (pow.f64 y 4) (pow.f64 (*.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (/.f64 1 (-.f64 (*.f64 x x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (pow.f64 y 4) (pow.f64 (*.f64 x y) 2))) (+.f64 (pow.f64 x 6) (pow.f64 y 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (-.f64 (pow.f64 x 4) (pow.f64 y 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 6)) (+.f64 (pow.f64 x 4) (-.f64 (pow.f64 y 4) (pow.f64 (*.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 6)) (+.f64 (pow.f64 y 4) (-.f64 (pow.f64 x 4) (pow.f64 (*.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (-.f64 (*.f64 x x) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 6))) (neg.f64 (+.f64 (pow.f64 x 4) (-.f64 (pow.f64 y 4) (pow.f64 (*.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4))) (neg.f64 (-.f64 (*.f64 x x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 y 4) (pow.f64 x 4)) (-.f64 (*.f64 y y) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x y) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (hypot.f64 x y) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x y) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x y) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (hypot.f64 x y) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (hypot.f64 x y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x y) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y y (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 y y) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 y 4)) (pow.f64 (cbrt.f64 y) 2) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 x y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (hypot.f64 x y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 x y) 2)))))))

simplify129.0ms (11.2%)

Algorithm
egg-herbie
Rules
1238×sqr-pow_binary64
754×cube-prod_binary64
730×fabs-mul_binary64
532×pow-sqr_binary64
346×unpow3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
07204
116168
229168
347168
499168
5269168
61081168
71364168
81642168
91893168
102230168
112711168
123366168
134154168
145078168
155593168
166004168
176395168
186508168
196552168
207721168
Stop Event
node limit
Counts
57 → 38
Calls
Call 1
Inputs
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
Outputs
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (*.f64 y y) (*.f64 x x))
(fma.f64 y y (*.f64 x x))

localize4.0ms (0.3%)

eval11.0ms (0.9%)

Compiler

Compiled 421 to 232 computations (44.9% saved)

prune6.0ms (0.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New36238
Fresh000
Picked011
Done011
Total36440
Error
0b
Counts
40 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
0b
(fma.f64 x x (*.f64 y y))
0.0b
(+.f64 (*.f64 x x) (*.f64 y y))
28.3b
(*.f64 x x)
28.5b
(*.f64 y y)
Compiler

Compiled 27 to 15 computations (44.4% saved)

localize2.0ms (0.1%)

localize2.0ms (0.1%)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done033
Total044
Error
0b
Counts
4 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
0b
(fma.f64 x x (*.f64 y y))
0.0b
(+.f64 (*.f64 x x) (*.f64 y y))
28.3b
(*.f64 x x)
28.5b
(*.f64 y y)
Compiler

Compiled 27 to 15 computations (44.4% saved)

regimes25.0ms (2.2%)

Counts
4 → 1
Calls
Call 1
Inputs
(*.f64 x x)
(*.f64 y y)
(+.f64 (*.f64 x x) (*.f64 y y))
(fma.f64 x x (*.f64 y y))
Outputs
(fma.f64 x x (*.f64 y y))
Calls

6 calls:

5.0ms
y
5.0ms
(*.f64 y y)
4.0ms
x
3.0ms
(+.f64 (*.f64 x x) (*.f64 y y))
3.0ms
(*.f64 x x)
Results
ErrorSegmentsBranch
0b1x
0b1y
0b1(+.f64 (*.f64 x x) (*.f64 y y))
0b1(*.f64 x x)
0b1(*.f64 x x)
0b1(*.f64 y y)
Compiler

Compiled 51 to 24 computations (52.9% saved)

regimes18.0ms (1.6%)

Counts
3 → 1
Calls
Call 1
Inputs
(*.f64 x x)
(*.f64 y y)
(+.f64 (*.f64 x x) (*.f64 y y))
Outputs
(+.f64 (*.f64 x x) (*.f64 y y))
Calls

5 calls:

5.0ms
(+.f64 (*.f64 x x) (*.f64 y y))
4.0ms
x
4.0ms
y
3.0ms
(*.f64 y y)
3.0ms
(*.f64 x x)
Results
ErrorSegmentsBranch
0.0b1x
0.0b1y
0.0b1(+.f64 (*.f64 x x) (*.f64 y y))
0.0b1(*.f64 x x)
0.0b1(*.f64 y y)
Compiler

Compiled 40 to 20 computations (50% saved)

regimes42.0ms (3.6%)

Accuracy

Total -49.9b remaining (-772.9%)

Threshold costs -49.9b (-772.9%)

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

4 calls:

16.0ms
y
10.0ms
x
10.0ms
(*.f64 y y)
5.0ms
(*.f64 x x)
Results
ErrorSegmentsBranch
7.4b2x
6.5b2y
9.9b2(*.f64 x x)
9.2b4(*.f64 y y)
Compiler

Compiled 24 to 14 computations (41.7% saved)

bsearch17.0ms (1.5%)

Algorithm
binary-search
Steps
TimeLeftRight
17.0ms
1.0016311354707272e-110
4.218626082396669e-104
Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify2.0ms (0.2%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01136
11236
Stop Event
saturated
Calls
Call 1
Inputs
(fma.f64 x x (*.f64 y y))
(+.f64 (*.f64 x x) (*.f64 y y))
(if (<=.f64 y 3390127312020881/338460656020607282663380637712778772392143197677711984273740183180495765112991409062496875745134225841966700556811959451779072) (*.f64 x x) (*.f64 y y))
(*.f64 x x)
Outputs
(fma.f64 x x (*.f64 y y))
(+.f64 (*.f64 x x) (*.f64 y y))
(+.f64 (*.f64 y y) (*.f64 x x))
(if (<=.f64 y 3390127312020881/338460656020607282663380637712778772392143197677711984273740183180495765112991409062496875745134225841966700556811959451779072) (*.f64 x x) (*.f64 y y))
(*.f64 x x)

end28.0ms (2.5%)

Stop Event
done
Remove

(sort x y)

Compiler

Compiled 78 to 36 computations (53.8% saved)

Profiling

Loading profile data...