Details

Time bar (total: 1.2s)

analyze57.0ms (4.9%)

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%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)

sample735.0ms (63.3%)

Results
724.0ms8256×body256valid
Bogosity

preprocess20.0ms (1.7%)

Algorithm
2×egg-herbie
Rules
96×fma-def
32×sub-neg
26×associate--r+
20×cancel-sign-sub-inv
16×neg-mul-1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01130
11530
22330
33630
46630
513130
616530
720530
821530
022
122
Stop Event
1×unsound
1×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)

simplify17.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
100×fma-def
32×sub-neg
24×associate--r+
20×cancel-sign-sub-inv
18×fabs-sub
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0815
11215
21915
32915
45015
510515
616915
720515
822815
923315
Stop Event
1×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
Accurracy
100.0%
Counts
2 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(sqrt.f64 (fabs.f64 (-.f64 x y)))
Compiler

Compiled 7 to 5 computations (28.6% saved)

localize6.0ms (0.5%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓100.0%
(sqrt.f64 (fabs.f64 (-.f64 x y)))
Compiler

Compiled 16 to 5 computations (68.8% saved)

series2.0ms (0.1%)

Counts
1 → 8
Calls

6 calls:

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

rewrite52.0ms (4.4%)

Algorithm
1×batch-egg-rewrite
Rules
1678×pow1
1556×add-exp-log
1556×log1p-expm1-u
1556×expm1-log1p-u
1520×add-log-exp
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0815
117111
2234511
Stop Event
1×node limit
Counts
1 → 22
Calls
Call 1
Inputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))
Outputs
(-.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 (cbrt.f64 (sqrt.f64 (-.f64 x y))) 3)
(pow.f64 (pow.f64 (-.f64 x y) 3/2) 1/3)
(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))))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 x y))))
(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 x y))))

simplify53.0ms (4.6%)

Algorithm
1×egg-herbie
Rules
790×fma-def
758×associate-*r*
648×associate-*l*
596×distribute-lft-in
554×distribute-rgt-in
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
075744
1156616
2372524
31172496
43972496
Stop Event
1×node limit
Counts
30 → 36
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 (cbrt.f64 (sqrt.f64 (-.f64 x y))) 3)
(pow.f64 (pow.f64 (-.f64 x y) 3/2) 1/3)
(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))))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 x y))))
(log1p.f64 (expm1.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 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (fma.f64 y y (*.f64 x (+.f64 y 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 (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) 3/2) 1/3)
(cbrt.f64 (pow.f64 (-.f64 x y) 3/2))
(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))
(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))
(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))

eval5.0ms (0.4%)

Compiler

Compiled 325 to 141 computations (56.6% saved)

prune6.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New35136
Fresh000
Picked011
Done000
Total35237
Accurracy
100.0%
Counts
37 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶0.0%
(sqrt.f64 (-.f64 x y))
✓100.0%
(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)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done011
Total022
Accurracy
100.0%
Counts
2 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓0.0%
(sqrt.f64 (-.f64 x y))
✓100.0%
(sqrt.f64 (fabs.f64 (-.f64 x y)))
Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes25.0ms (2.2%)

Accuracy

Total -64.0b remaining (-819100%)

Threshold costs -64b (-819100%)

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:

4.0ms
(fabs.f64 (-.f64 x y))
3.0ms
x
3.0ms
(sqrt.f64 (fabs.f64 (-.f64 x y)))
3.0ms
(-.f64 x y)
3.0ms
y
Results
AccuracySegmentsBranch
100.0%1x
100.0%1y
100.0%1(sqrt.f64 (fabs.f64 (-.f64 x y)))
100.0%1(fabs.f64 (-.f64 x y))
100.0%1(-.f64 x y)
Compiler

Compiled 35 to 22 computations (37.1% saved)

simplify4.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
8×sub-neg
8×+-commutative
4×neg-mul-1
4×*-commutative
4×neg-sub0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0926
11326
22026
32526
42826
52926
Stop Event
1×done
1×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)

soundness159.0ms (13.7%)

Rules
1678×pow1
1556×add-exp-log
1556×log1p-expm1-u
1556×expm1-log1p-u
1520×add-log-exp
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0815
117111
2234511
075744
1156616
2372524
31172496
43972496
Stop Event
1×node limit
1×node limit
Compiler

Compiled 116 to 55 computations (52.6% saved)

end15.0ms (1.3%)

Remove

(sort x y)

Compiler

Compiled 25 to 16 computations (36% saved)

Profiling

Loading profile data...