Details

Time bar (total: 1.0s)

analyze54.0ms (5.2%)

Algorithm
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%99.9%0.1%0%0%0%4
25%25%74.9%0.1%0%0%0%5
37.5%37.5%62.4%0.1%0%0%0%6
56.3%56.2%43.7%0.1%0%0%0%7
65.6%65.6%34.3%0.1%0%0%0%8
76.6%76.5%23.4%0.1%0%0%0%9
82%82%18%0.1%0%0%0%10
87.9%87.8%12.1%0.1%0%0%0%11
90.8%90.7%9.2%0.1%0%0%0%12
Compiler

Compiled 8 to 6 computations (25% saved)

sample752.0ms (72.9%)

Results
740.0ms8256×body256valid
Bogosity

preprocess18.0ms (1.7%)

Algorithm
egg-herbie
Rules
36×fma-neg_binary64
16×sub-neg_binary64
16×fma-def_binary64
14×cancel-sign-sub-inv_binary64
associate--r+_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0916
11316
22116
33316
46316
511616
615016
719216
820216
022
122
Stop Event
unsound
saturated
Calls
Call 1
Inputs
0
1
Outputs
0
1
0
Call 2
Inputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
Outputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt.f64 (fabs.f64 (-.f64 x y)))
Symmetry

(sort x y)

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify10.0ms (0.9%)

Algorithm
egg-herbie
Rules
39×fma-neg_binary64
17×fma-def_binary64
16×cancel-sign-sub-inv_binary64
16×sub-neg_binary64
fabs-sub_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1108
2178
3268
4478
51038
61548
71938
82188
92238
Stop Event
saturated
Counts
1 → 1
Calls
Call 1
Inputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))
Outputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))

eval0.0ms (0%)

Compiler

Compiled 7 to 5 computations (28.6% 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 (fabs.f64 (-.f64 x y)))
Compiler

Compiled 7 to 5 computations (28.6% saved)

localize19.0ms (1.8%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (fabs.f64 (-.f64 x y)))
Compiler

Compiled 16 to 5 computations (68.8% saved)

series3.0ms (0.2%)

Counts
1 → 8
Calls

6 calls:

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

rewrite61.0ms (5.9%)

Algorithm
batch-egg-rewrite
Rules
664×pow1_binary64
621×add-log-exp_binary64
621×log1p-expm1-u_binary64
621×expm1-log1p-u_binary64
607×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
068
11336
219066
Stop Event
node limit
Counts
1 → 22
Calls
Call 1
Inputs
(sqrt.f64 (fabs.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 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (fma.f64 x x (*.f64 y (+.f64 x y)))))))) (#(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) 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 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))))))))

simplify41.0ms (3.9%)

Algorithm
egg-herbie
Rules
373×associate-*l*_binary64
345×fma-neg_binary64
334×associate-*r*_binary64
310×distribute-rgt-in_binary64
283×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
072387
1153323
2371277
31185263
44033263
Stop Event
node limit
Counts
30 → 35
Calls
Call 1
Inputs
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (*.f64 -1 x)))))
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (*.f64 -1 x)))))
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (*.f64 -1 x)))))
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (*.f64 -1 x)))))
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 -1 y) x)))
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 -1 y) x)))
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 -1 y) x)))
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 -1 y) 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 (cbrt.f64 (sqrt.f64 (-.f64 x y))) (cbrt.f64 (-.f64 x y)))
(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (sqrt.f64 (-.f64 x y))))
(*.f64 (pow.f64 (-.f64 x y) 1/4) (pow.f64 (-.f64 x y) 1/4))
(*.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 x y)))))
(/.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) 3/2) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 x y))) 3)
(pow.f64 (pow.f64 (-.f64 x y) 1/4) 2)
(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))))
(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 x y))))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 x y))))
Outputs
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (*.f64 -1 x)))))
(sqrt.f64 (fabs.f64 (+.f64 y (neg.f64 x))))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (*.f64 -1 x)))))
(sqrt.f64 (fabs.f64 (+.f64 y (neg.f64 x))))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (*.f64 -1 x)))))
(sqrt.f64 (fabs.f64 (+.f64 y (neg.f64 x))))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (*.f64 -1 x)))))
(sqrt.f64 (fabs.f64 (+.f64 y (neg.f64 x))))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 -1 y) x)))
(sqrt.f64 (fabs.f64 (+.f64 y (neg.f64 x))))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 -1 y) x)))
(sqrt.f64 (fabs.f64 (+.f64 y (neg.f64 x))))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 -1 y) x)))
(sqrt.f64 (fabs.f64 (+.f64 y (neg.f64 x))))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 -1 y) x)))
(sqrt.f64 (fabs.f64 (+.f64 y (neg.f64 x))))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(-.f64 (+.f64 1 (sqrt.f64 (-.f64 x y))) 1)
(+.f64 (+.f64 1 (sqrt.f64 (-.f64 x y))) -1)
(+.f64 (sqrt.f64 (-.f64 x y)) 0)
(sqrt.f64 (-.f64 x y))
(*.f64 (sqrt.f64 (-.f64 x y)) 1)
(+.f64 (+.f64 1 (sqrt.f64 (-.f64 x y))) -1)
(+.f64 (sqrt.f64 (-.f64 x y)) 0)
(sqrt.f64 (-.f64 x y))
(*.f64 1 (sqrt.f64 (-.f64 x y)))
(+.f64 (+.f64 1 (sqrt.f64 (-.f64 x y))) -1)
(+.f64 (sqrt.f64 (-.f64 x y)) 0)
(sqrt.f64 (-.f64 x y))
(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 x y))) (cbrt.f64 (-.f64 x y)))
(*.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 (pow.f64 (-.f64 x y) 1/4) (pow.f64 (-.f64 x y) 1/4))
(+.f64 (+.f64 1 (sqrt.f64 (-.f64 x y))) -1)
(+.f64 (sqrt.f64 (-.f64 x y)) 0)
(sqrt.f64 (-.f64 x y))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 x y)) 2)) (sqrt.f64 (cbrt.f64 (-.f64 x y))))
(*.f64 (fabs.f64 (cbrt.f64 (-.f64 x y))) (sqrt.f64 (cbrt.f64 (-.f64 x y))))
(*.f64 (cbrt.f64 (-.f64 x y)) (sqrt.f64 (cbrt.f64 (-.f64 x y))))
(pow.f64 (cbrt.f64 (-.f64 x y)) 3/2)
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 x y)))
(+.f64 (+.f64 1 (sqrt.f64 (-.f64 x y))) -1)
(+.f64 (sqrt.f64 (-.f64 x y)) 0)
(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 (pow.f64 (cbrt.f64 (-.f64 x y)) 2)) (sqrt.f64 (cbrt.f64 (-.f64 x y))))
(*.f64 (fabs.f64 (cbrt.f64 (-.f64 x y))) (sqrt.f64 (cbrt.f64 (-.f64 x y))))
(*.f64 (cbrt.f64 (-.f64 x y)) (sqrt.f64 (cbrt.f64 (-.f64 x y))))
(pow.f64 (cbrt.f64 (-.f64 x y)) 3/2)
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (fma.f64 x x (*.f64 y (+.f64 x y)))))
(/.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 x 3) (pow.f64 y 3))) (sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 y y))) (sqrt.f64 (+.f64 x y)))
(/.f64 (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 y y))) (sqrt.f64 (+.f64 y x)))
(pow.f64 (-.f64 x y) 1/2)
(+.f64 (+.f64 1 (sqrt.f64 (-.f64 x y))) -1)
(+.f64 (sqrt.f64 (-.f64 x y)) 0)
(sqrt.f64 (-.f64 x y))
(pow.f64 (sqrt.f64 (-.f64 x y)) 1)
(+.f64 (+.f64 1 (sqrt.f64 (-.f64 x y))) -1)
(+.f64 (sqrt.f64 (-.f64 x y)) 0)
(sqrt.f64 (-.f64 x y))
(pow.f64 (pow.f64 (-.f64 x y) 3/2) 1/3)
(cbrt.f64 (pow.f64 (-.f64 x y) 3/2))
(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 x y))) 3)
(+.f64 (+.f64 1 (sqrt.f64 (-.f64 x y))) -1)
(+.f64 (sqrt.f64 (-.f64 x y)) 0)
(sqrt.f64 (-.f64 x y))
(pow.f64 (pow.f64 (-.f64 x y) 1/4) 2)
(+.f64 (+.f64 1 (sqrt.f64 (-.f64 x y))) -1)
(+.f64 (sqrt.f64 (-.f64 x y)) 0)
(sqrt.f64 (-.f64 x y))
(fabs.f64 (sqrt.f64 (-.f64 x y)))
(+.f64 (+.f64 1 (sqrt.f64 (-.f64 x y))) -1)
(+.f64 (sqrt.f64 (-.f64 x y)) 0)
(sqrt.f64 (-.f64 x y))
(log.f64 (exp.f64 (sqrt.f64 (-.f64 x y))))
(+.f64 (+.f64 1 (sqrt.f64 (-.f64 x y))) -1)
(+.f64 (sqrt.f64 (-.f64 x y)) 0)
(sqrt.f64 (-.f64 x y))
(cbrt.f64 (pow.f64 (-.f64 x y) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 x y))))
(+.f64 (+.f64 1 (sqrt.f64 (-.f64 x y))) -1)
(+.f64 (sqrt.f64 (-.f64 x y)) 0)
(sqrt.f64 (-.f64 x y))
(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 x y))))
(+.f64 (+.f64 1 (sqrt.f64 (-.f64 x y))) -1)
(+.f64 (sqrt.f64 (-.f64 x y)) 0)
(sqrt.f64 (-.f64 x y))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 x y))))
(+.f64 (+.f64 1 (sqrt.f64 (-.f64 x y))) -1)
(+.f64 (sqrt.f64 (-.f64 x y)) 0)
(sqrt.f64 (-.f64 x y))

eval4.0ms (0.4%)

Compiler

Compiled 307 to 131 computations (57.3% saved)

prune5.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New34135
Fresh000
Picked011
Done000
Total34236
Error
0.0b
Counts
36 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
64.0b
(sqrt.f64 (-.f64 x y))
0.0b
(sqrt.f64 (fabs.f64 (-.f64 x y)))
Compiler

Compiled 13 to 9 computations (30.8% saved)

localize4.0ms (0.4%)

Compiler

Compiled 11 to 4 computations (63.6% saved)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune28.0ms (2.7%)

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
64.0b
(sqrt.f64 (-.f64 x y))
0.0b
(sqrt.f64 (fabs.f64 (-.f64 x y)))
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes16.0ms (1.6%)

Accuracy

Total -64.0b remaining (-546033.3%)

Threshold costs -64.0b (-546033.3%)

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

5 calls:

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

Compiled 35 to 22 computations (37.1% saved)

simplify3.0ms (0.2%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
sub-neg_binary64
*-commutative_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0714
11114
21814
32314
42614
52714
Stop Event
done
saturated
Calls
Call 1
Inputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(sqrt.f64 (-.f64 x y))
Outputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(sqrt.f64 (-.f64 x y))
Compiler

Compiled 13 to 9 computations (30.8% saved)

soundness0.0ms (0%)

end14.0ms (1.4%)

Remove

(sort x y)

Compiler

Compiled 25 to 16 computations (36% saved)

Profiling

Loading profile data...