Linear.Quaternion:$clog from linear-1.19.1.3

Time bar (total: 1.3s)

analyze18.0ms (1.3%)

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
50%50%50%0.1%0%0%0%3
50%50%50%0.1%0%0%0%4
62.5%62.4%37.5%0.1%0%0%0%5
66.7%62.4%31.2%0.1%0%6.2%0%6
75%65.6%21.9%0.1%0%12.5%0%7
80%68.7%17.2%0.1%0%14%0%8
85.7%70.2%11.7%0.1%0%18%0%9
88.9%71.8%9%0.1%0%19.1%0%10
92.3%72.6%6%0.1%0%21.3%0%11
94.1%73.4%4.6%0.1%0%22%0%12
Compiler

Compiled 9 to 6 computations (33.3% saved)

sample863.0ms (65%)

Results
805.0ms8256×body256valid
47.0ms331×body256invalid
Bogosity

preprocess31.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
308×fma-def
60×fma-neg
48×sub-neg
32×distribute-lft-neg-in
32×associate--r+
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01856
13756
27056
314456
424256
532956
642256
747656
849056
949356
Stop Event
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
(sqrt.f64 (+.f64 (*.f64 (neg.f64 x) (neg.f64 x)) y))
(sqrt.f64 (+.f64 (*.f64 x x) (neg.f64 y)))
(sqrt.f64 (+.f64 (*.f64 y y) x))
Outputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
(sqrt.f64 (fma.f64 x x y))
(sqrt.f64 (+.f64 (*.f64 (neg.f64 x) (neg.f64 x)) y))
(sqrt.f64 (fma.f64 x x y))
(sqrt.f64 (+.f64 (*.f64 x x) (neg.f64 y)))
(sqrt.f64 (fma.f64 x x (neg.f64 y)))
(sqrt.f64 (-.f64 (*.f64 x x) y))
(sqrt.f64 (+.f64 (*.f64 y y) x))
(sqrt.f64 (fma.f64 y y x))
Symmetry

(abs x)

Compiler

Compiled 10 to 7 computations (30% saved)

simplify3.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
2×fma-def
2×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
11113
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
Outputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
(sqrt.f64 (fma.f64 x x y))

eval0.0ms (0%)

Compiler

Compiled 13 to 7 computations (46.2% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Accurracy
67.7%
Counts
3 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶67.7%
(sqrt.f64 (+.f64 (*.f64 x x) y))
▶67.7%
(sqrt.f64 (+.f64 (*.f64 x x) y))
Compiler

Compiled 16 to 10 computations (37.5% saved)

localize29.0ms (2.2%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓67.7%
(sqrt.f64 (+.f64 (*.f64 x x) y))
Compiler

Compiled 19 to 6 computations (68.4% saved)

series2.0ms (0.2%)

Counts
1 → 16
Calls

6 calls:

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

rewrite85.0ms (6.4%)

Algorithm
1×batch-egg-rewrite
Rules
1692×pow1
1568×add-exp-log
1568×log1p-expm1-u
1568×expm1-log1p-u
1534×add-log-exp
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0813
116911
2221011
Stop Event
1×node limit
Counts
1 → 24
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
Outputs
(-.f64 (+.f64 1 (hypot.f64 x (sqrt.f64 y))) 1)
(*.f64 (hypot.f64 x (sqrt.f64 y)) 1)
(*.f64 1 (hypot.f64 x (sqrt.f64 y)))
(*.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (cbrt.f64 (hypot.f64 x (sqrt.f64 y))))
(*.f64 (pow.f64 (fma.f64 x x y) 1/4) (pow.f64 (fma.f64 x x y) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (pow.f64 1 1/2) (hypot.f64 x (sqrt.f64 y)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 1/2))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x 4) (*.f64 y y))) (sqrt.f64 (-.f64 (*.f64 x x) y)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 y 3) (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) (*.f64 y (-.f64 y (*.f64 x x))))))
(pow.f64 (fma.f64 x x y) 1/2)
(pow.f64 (hypot.f64 x (sqrt.f64 y)) 1)
(pow.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) 3)
(pow.f64 (pow.f64 (fma.f64 x x y) 3/2) 1/3)
(pow.f64 (pow.f64 (fma.f64 x x y) 1/4) 2)
(fabs.f64 (hypot.f64 x (sqrt.f64 y)))
(log.f64 (exp.f64 (hypot.f64 x (sqrt.f64 y))))
(cbrt.f64 (pow.f64 (fma.f64 x x y) 3/2))
(expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 y))))
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(exp.f64 (log.f64 (hypot.f64 x (sqrt.f64 y))))
(log1p.f64 (expm1.f64 (hypot.f64 x (sqrt.f64 y))))

simplify72.0ms (5.4%)

Algorithm
1×egg-herbie
Rules
1528×times-frac
1390×fma-neg
1162×associate-/l*
740×associate-/r*
678×*-commutative
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01171280
12701160
27021056
323991020
476611020
Stop Event
1×node limit
Counts
40 → 68
Calls
Call 1
Inputs
(sqrt.f64 y)
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y))
(+.f64 (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y)))
(+.f64 (*.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 6))) (+.f64 (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y))))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(+.f64 (*.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x))
(+.f64 (*.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (*.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
(*.f64 -1 x)
(+.f64 (*.f64 -1/2 (/.f64 y x)) (*.f64 -1 x))
(+.f64 (*.f64 -1/2 (/.f64 y x)) (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))))
(+.f64 (*.f64 -1/2 (/.f64 y x)) (+.f64 (*.f64 -1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(+.f64 (*.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x))
(+.f64 (*.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (*.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
(-.f64 (+.f64 1 (hypot.f64 x (sqrt.f64 y))) 1)
(*.f64 (hypot.f64 x (sqrt.f64 y)) 1)
(*.f64 1 (hypot.f64 x (sqrt.f64 y)))
(*.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (cbrt.f64 (hypot.f64 x (sqrt.f64 y))))
(*.f64 (pow.f64 (fma.f64 x x y) 1/4) (pow.f64 (fma.f64 x x y) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (pow.f64 1 1/2) (hypot.f64 x (sqrt.f64 y)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 1/2))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x 4) (*.f64 y y))) (sqrt.f64 (-.f64 (*.f64 x x) y)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 y 3) (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) (*.f64 y (-.f64 y (*.f64 x x))))))
(pow.f64 (fma.f64 x x y) 1/2)
(pow.f64 (hypot.f64 x (sqrt.f64 y)) 1)
(pow.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) 3)
(pow.f64 (pow.f64 (fma.f64 x x y) 3/2) 1/3)
(pow.f64 (pow.f64 (fma.f64 x x y) 1/4) 2)
(fabs.f64 (hypot.f64 x (sqrt.f64 y)))
(log.f64 (exp.f64 (hypot.f64 x (sqrt.f64 y))))
(cbrt.f64 (pow.f64 (fma.f64 x x y) 3/2))
(expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 y))))
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(exp.f64 (log.f64 (hypot.f64 x (sqrt.f64 y))))
(log1p.f64 (expm1.f64 (hypot.f64 x (sqrt.f64 y))))
Outputs
(sqrt.f64 y)
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y))
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x x)) (sqrt.f64 y))
(+.f64 (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y)))
(fma.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4)) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x x)) (sqrt.f64 y)))
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x x)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 -1/8 (pow.f64 x 4)) (sqrt.f64 y)))
(+.f64 (*.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 6))) (+.f64 (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y))))
(fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 6)) (fma.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4)) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x x)) (sqrt.f64 y))))
(fma.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4)) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 6)) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x x)) (sqrt.f64 y))))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(fma.f64 1/2 (/.f64 y x) x)
(+.f64 (*.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x))
(+.f64 (*.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (*.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x)))
(fma.f64 1/2 (/.f64 y x) (fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x)))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (*.f64 -1/2 (/.f64 y x)) (*.f64 -1 x))
(fma.f64 -1/2 (/.f64 y x) (neg.f64 x))
(-.f64 (*.f64 (/.f64 y x) -1/2) x)
(neg.f64 (fma.f64 1/2 (/.f64 y x) x))
(+.f64 (*.f64 -1/2 (/.f64 y x)) (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 y x) (fma.f64 -1 x (*.f64 (/.f64 (*.f64 y y) (pow.f64 x 3)) 1/8)))
(fma.f64 (/.f64 y x) -1/2 (-.f64 (*.f64 (/.f64 y (/.f64 (pow.f64 x 3) y)) 1/8) x))
(-.f64 (fma.f64 (/.f64 y x) -1/2 (*.f64 (/.f64 y (/.f64 (pow.f64 x 3) y)) 1/8)) x)
(-.f64 (*.f64 (/.f64 y x) (+.f64 -1/2 (*.f64 (/.f64 y x) (/.f64 1/8 x)))) x)
(+.f64 (*.f64 -1/2 (/.f64 y x)) (+.f64 (*.f64 -1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))))
(fma.f64 -1/2 (/.f64 y x) (fma.f64 -1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1 x (*.f64 (/.f64 (*.f64 y y) (pow.f64 x 3)) 1/8))))
(fma.f64 (/.f64 y x) -1/2 (fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) -1/16 (-.f64 (*.f64 (/.f64 y (/.f64 (pow.f64 x 3) y)) 1/8) x)))
(fma.f64 (/.f64 y x) -1/2 (-.f64 (fma.f64 (/.f64 y (/.f64 (pow.f64 x 3) y)) 1/8 (/.f64 (*.f64 (pow.f64 y 3) -1/16) (pow.f64 x 5))) x))
(fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) -1/16 (-.f64 (*.f64 (/.f64 y x) (+.f64 -1/2 (*.f64 (/.f64 y x) (/.f64 1/8 x)))) x))
(fma.f64 (/.f64 y x) (+.f64 -1/2 (*.f64 (/.f64 y x) (/.f64 1/8 x))) (-.f64 (/.f64 (pow.f64 y 3) (/.f64 (pow.f64 x 5) -1/16)) x))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(fma.f64 1/2 (/.f64 y x) x)
(+.f64 (*.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x))
(+.f64 (*.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (*.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x)))
(fma.f64 1/2 (/.f64 y x) (fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x)))
(-.f64 (+.f64 1 (hypot.f64 x (sqrt.f64 y))) 1)
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(*.f64 (hypot.f64 x (sqrt.f64 y)) 1)
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(*.f64 1 (hypot.f64 x (sqrt.f64 y)))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(*.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 y) x)) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (cbrt.f64 (hypot.f64 x (sqrt.f64 y))))
(*.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 y) x)) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (pow.f64 (fma.f64 x x y) 1/4) (pow.f64 (fma.f64 x x y) 1/4))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x y))) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(pow.f64 (cbrt.f64 (fma.f64 x x y)) 3/2)
(*.f64 (pow.f64 1 1/2) (hypot.f64 x (sqrt.f64 y)))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x y))) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(pow.f64 (cbrt.f64 (fma.f64 x x y)) 3/2)
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x 4) (*.f64 y y))) (sqrt.f64 (-.f64 (*.f64 x x) y)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 y 3) (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) (*.f64 y (-.f64 y (*.f64 x x))))))
(/.f64 (hypot.f64 (pow.f64 x 3) (pow.f64 y 3/2)) (sqrt.f64 (fma.f64 y (-.f64 y (*.f64 x x)) (pow.f64 x 4))))
(/.f64 (hypot.f64 (pow.f64 x 3) (pow.f64 y 3/2)) (sqrt.f64 (fma.f64 y (fma.f64 x (neg.f64 x) y) (pow.f64 x 4))))
(pow.f64 (fma.f64 x x y) 1/2)
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(pow.f64 (hypot.f64 x (sqrt.f64 y)) 1)
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(pow.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) 3)
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(pow.f64 (pow.f64 (fma.f64 x x y) 3/2) 1/3)
(cbrt.f64 (pow.f64 (fma.f64 x x y) 3/2))
(pow.f64 (pow.f64 (fma.f64 x x y) 1/4) 2)
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(fabs.f64 (hypot.f64 x (sqrt.f64 y)))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(log.f64 (exp.f64 (hypot.f64 x (sqrt.f64 y))))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(cbrt.f64 (pow.f64 (fma.f64 x x y) 3/2))
(expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 y))))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(hypot.f64 x (sqrt.f64 y))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(hypot.f64 (sqrt.f64 y) x)
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(exp.f64 (log.f64 (hypot.f64 x (sqrt.f64 y))))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(log1p.f64 (expm1.f64 (hypot.f64 x (sqrt.f64 y))))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)

eval25.0ms (1.9%)

Compiler

Compiled 950 to 526 computations (44.6% saved)

prune12.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New65368
Fresh000
Picked011
Done000
Total65469
Accurracy
100.0%
Counts
69 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶69.9%
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓67.7%
(sqrt.f64 (+.f64 (*.f64 x x) y))
▶33.1%
(sqrt.f64 y)
69.4%
x
▶69.9%
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓67.7%
(sqrt.f64 (+.f64 (*.f64 x x) y))
▶33.1%
(sqrt.f64 y)
69.4%
x
Compiler

Compiled 48 to 32 computations (33.3% saved)

localize31.0ms (2.4%)

Compiler

Compiled 24 to 11 computations (54.2% saved)

eval1.0ms (0.1%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune3.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New000
Fresh011
Picked022
Done011
Total044
Accurracy
100.0%
Counts
4 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓69.9%
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓67.7%
(sqrt.f64 (+.f64 (*.f64 x x) y))
✓33.1%
(sqrt.f64 y)
69.4%
x
✓69.9%
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓67.7%
(sqrt.f64 (+.f64 (*.f64 x x) y))
✓33.1%
(sqrt.f64 y)
69.4%
x
Compiler

Compiled 48 to 32 computations (33.3% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune3.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done033
Total044
Accurracy
100.0%
Counts
4 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓69.9%
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓67.7%
(sqrt.f64 (+.f64 (*.f64 x x) y))
✓33.1%
(sqrt.f64 y)
69.4%
x
✓69.9%
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓67.7%
(sqrt.f64 (+.f64 (*.f64 x x) y))
✓33.1%
(sqrt.f64 y)
69.4%
x
Compiler

Compiled 48 to 32 computations (33.3% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done033
Total044
Accurracy
100.0%
Counts
4 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓69.9%
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓67.7%
(sqrt.f64 (+.f64 (*.f64 x x) y))
✓33.1%
(sqrt.f64 y)
69.4%
x
Compiler

Compiled 42 to 26 computations (38.1% saved)

regimes44.0ms (3.3%)

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

5 calls:

15.0ms
y
8.0ms
x
7.0ms
(sqrt.f64 (+.f64 (*.f64 x x) y))
7.0ms
(+.f64 (*.f64 x x) y)
6.0ms
(*.f64 x x)
Results
AccuracySegmentsBranch
100.0%2x
87.9%4y
100.0%2(sqrt.f64 (+.f64 (*.f64 x x) y))
100.0%2(+.f64 (*.f64 x x) y)
100.0%2(*.f64 x x)
Compiler

Compiled 44 to 26 computations (40.9% saved)

regimes8.0ms (0.6%)

Counts
3 → 2
Calls
Call 1
Inputs
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(sqrt.f64 y)
Outputs
(sqrt.f64 y)
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
Calls

1 calls:

7.0ms
x
Results
AccuracySegmentsBranch
92.5%2x
Compiler

Compiled 15 to 9 computations (40% saved)

regimes8.0ms (0.6%)

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

2 calls:

4.0ms
y
3.0ms
x
Results
AccuracySegmentsBranch
69.9%1y
69.9%1x
Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes6.0ms (0.4%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
x
Outputs
x
Calls

2 calls:

3.0ms
x
3.0ms
y
Results
AccuracySegmentsBranch
69.4%1x
69.4%1y
Compiler

Compiled 9 to 6 computations (33.3% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.331838717148617e+205
6.745430375428217e+224
Compiler

Compiled 13 to 9 computations (30.8% saved)

bsearch19.0ms (1.4%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
18.0ms
1.096957351390281e-32
5.361526211099146e-28
Results
15.0ms128×body256valid
2.0ms23×body256invalid
Compiler

Compiled 133 to 97 computations (27.1% saved)

simplify7.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
4×+-commutative
2×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02286
12586
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 (*.f64 x x) 20000000000000000332320709457100266805720535239871327970256129990546078137252710026514902573853139251497244082176191898637596077985558673396359852997433671054025460248400909387429436243536565212333765296128) (sqrt.f64 (+.f64 (*.f64 x x) y)) x)
(if (<=.f64 x 35681192317649/11150372599265311570767859136324180752990208) (sqrt.f64 y) (+.f64 (*.f64 1/2 (/.f64 y x)) x))
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
x
Outputs
(if (<=.f64 (*.f64 x x) 20000000000000000332320709457100266805720535239871327970256129990546078137252710026514902573853139251497244082176191898637596077985558673396359852997433671054025460248400909387429436243536565212333765296128) (sqrt.f64 (+.f64 (*.f64 x x) y)) x)
(if (<=.f64 x 35681192317649/11150372599265311570767859136324180752990208) (sqrt.f64 y) (+.f64 (*.f64 1/2 (/.f64 y x)) x))
(if (<=.f64 x 35681192317649/11150372599265311570767859136324180752990208) (sqrt.f64 y) (+.f64 x (*.f64 1/2 (/.f64 y x))))
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(+.f64 x (*.f64 1/2 (/.f64 y x)))
x
Compiler

Compiled 42 to 26 computations (38.1% saved)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess53.0ms (4%)

Compiler

Compiled 180 to 102 computations (43.3% saved)

Profiling

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