sqrt E (should all be same)

Time bar (total: 5.0s)

analyze1.6s (32.1%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%199.9%-99.9%0%0%0%1
0%0%399.8%-299.8%0%0%0%2
0%0%799.6%-699.6%0%0%0%3
0%0%1599.2%-1499.2%0%0%0%4
0%0%3198.4%-3098.4%0%0%0%5
0%0%6396.9%-6296.9%0%0%0%6
0%0%12793.8%-12693.8%0%0%0%7
0%0%25587.5%-25487.5%0%0%0%8
0%0%51175%-51075%0%0%0%9
0%0%102350%-102250%0%0%0%10
0%0%204700%-204600%0%0%0%11
0%0%409400%-409300%0%0%0%12
Compiler

Compiled 10 to 8 computations (20% saved)

sample2.5s (50.1%)

Results
2.5s8253×body256valid
1.0ms3×body256infinite
Bogosity

preprocess101.0ms (2%)

Algorithm
1×egg-herbie
Rules
1068×fma-neg
982×distribute-lft-out
896×fma-def
886×hypot-def
744×distribute-lft-neg-in
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01234
12614
26814
323514
4104714
5282914
6583014
7789414
Stop Event
1×node limit
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (+.f64 (pow.f64 (neg.f64 x) 2) (pow.f64 (neg.f64 x) 2)))
Outputs
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (*.f64 2 (*.f64 x x)))
(hypot.f64 x x)
(sqrt.f64 (+.f64 (pow.f64 (neg.f64 x) 2) (pow.f64 (neg.f64 x) 2)))
(sqrt.f64 (*.f64 2 (*.f64 x x)))
(hypot.f64 x x)
Symmetry

(abs x)

Compiler

Compiled 10 to 8 computations (20% saved)

simplify131.0ms (2.6%)

Algorithm
1×egg-herbie
Rules
2556×fma-def
1482×distribute-lft-out
1118×hypot-def
988×count-2
868×unswap-sqr
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0817
1147
2337
3567
41217
53807
613817
725897
839327
948607
1056267
1166377
1274947
Stop Event
1×node limit
Counts
1 → 3
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
Outputs
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (*.f64 2 (*.f64 x x)))
(hypot.f64 x x)

eval1.0ms (0%)

Compiler

Compiled 18 to 12 computations (33.3% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New213
Fresh101
Picked000
Done000
Total314
Accurracy
100.0%
Counts
4 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(hypot.f64 x x)
▶100.0%
(hypot.f64 x x)
Compiler

Compiled 8 to 4 computations (50% saved)

localize20.0ms (0.4%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓100.0%
(hypot.f64 x x)
Compiler

Compiled 6 to 3 computations (50% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(hypot.f64 x x)
1.0ms
x
@inf
(hypot.f64 x x)
1.0ms
x
@0
(hypot.f64 x x)

rewrite53.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
738×pow1
704×add-sqr-sqrt
696×*-un-lft-identity
674×add-exp-log
674×log1p-expm1-u
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047
1807
29337
Stop Event
1×node limit
Counts
1 → 41
Calls
Call 1
Inputs
(hypot.f64 x x)
Outputs
(+.f64 0 (hypot.f64 x x))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(-.f64 (+.f64 1 (hypot.f64 x x)) 1)
(*.f64 (hypot.f64 x x) 1)
(*.f64 1 (hypot.f64 x x))
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2))
(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 1 1/3) (hypot.f64 x x))
(*.f64 (pow.f64 1 1/2) (hypot.f64 x x))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(*.f64 (pow.f64 (pow.f64 (*.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 2 1/2) x)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(pow.f64 (hypot.f64 x x) 1)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(pow.f64 (*.f64 x (+.f64 x x)) 1/2)
(pow.f64 (E.f64) (log.f64 (hypot.f64 x x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (log.f64 (hypot.f64 x x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 x x)))) (sqrt.f64 (log.f64 (hypot.f64 x x))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(exp.f64 (log.f64 (hypot.f64 x x)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (hypot.f64 x x))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 2))
(exp.f64 (*.f64 (*.f64 2 (log.f64 (hypot.f64 x x))) 1/2))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))

simplify56.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
924×associate-*r*
884×log-prod
766×associate-*l*
738×associate-+r+
718×associate-+l+
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0116717
1249681
2686669
34006669
Stop Event
1×node limit
Counts
53 → 55
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(+.f64 0 (hypot.f64 x x))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(-.f64 (+.f64 1 (hypot.f64 x x)) 1)
(*.f64 (hypot.f64 x x) 1)
(*.f64 1 (hypot.f64 x x))
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2))
(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 1 1/3) (hypot.f64 x x))
(*.f64 (pow.f64 1 1/2) (hypot.f64 x x))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(*.f64 (pow.f64 (pow.f64 (*.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 2 1/2) x)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(pow.f64 (hypot.f64 x x) 1)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(pow.f64 (*.f64 x (+.f64 x x)) 1/2)
(pow.f64 (E.f64) (log.f64 (hypot.f64 x x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (log.f64 (hypot.f64 x x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 x x)))) (sqrt.f64 (log.f64 (hypot.f64 x x))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(exp.f64 (log.f64 (hypot.f64 x x)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (hypot.f64 x x))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 2))
(exp.f64 (*.f64 (*.f64 2 (log.f64 (hypot.f64 x x))) 1/2))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(+.f64 0 (hypot.f64 x x))
(hypot.f64 x x)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))))
(hypot.f64 x x)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(*.f64 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))) 3)
(-.f64 (+.f64 1 (hypot.f64 x x)) 1)
(hypot.f64 x x)
(*.f64 (hypot.f64 x x) 1)
(hypot.f64 x x)
(*.f64 1 (hypot.f64 x x))
(hypot.f64 x x)
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
(hypot.f64 x x)
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2))
(hypot.f64 x x)
(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2))
(hypot.f64 x x)
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/2)))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (*.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 8)))
(*.f64 (pow.f64 1 1/3) (hypot.f64 x x))
(hypot.f64 x x)
(*.f64 (pow.f64 1 1/2) (hypot.f64 x x))
(hypot.f64 x x)
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(hypot.f64 x x)
(*.f64 (pow.f64 (pow.f64 (*.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (*.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 8)))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/2)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(hypot.f64 x x)
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
(hypot.f64 x x)
(*.f64 (pow.f64 2 1/2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(hypot.f64 x x)
(pow.f64 (hypot.f64 x x) 1)
(hypot.f64 x x)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(hypot.f64 x x)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(hypot.f64 x x)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(hypot.f64 x x)
(pow.f64 (*.f64 x (+.f64 x x)) 1/2)
(hypot.f64 x x)
(pow.f64 (E.f64) (log.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (log.f64 (hypot.f64 x x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 x x)))) (sqrt.f64 (log.f64 (hypot.f64 x x))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(hypot.f64 x x)
(log.f64 (exp.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(hypot.f64 x x)
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(exp.f64 (log.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(hypot.f64 x x)
(exp.f64 (*.f64 (*.f64 3 (log.f64 (hypot.f64 x x))) 1/3))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 2))
(hypot.f64 x x)
(exp.f64 (*.f64 (*.f64 2 (log.f64 (hypot.f64 x x))) 1/2))
(hypot.f64 x x)
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(hypot.f64 x x)

eval9.0ms (0.2%)

Compiler

Compiled 507 to 205 computations (59.6% saved)

prune39.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New54155
Fresh000
Picked011
Done000
Total54256
Accurracy
100.0%
Counts
56 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(hypot.f64 x x)
▶99.4%
(*.f64 (sqrt.f64 2) x)
✓100.0%
(hypot.f64 x x)
▶99.4%
(*.f64 (sqrt.f64 2) x)
Compiler

Compiled 18 to 12 computations (33.3% saved)

localize33.0ms (0.7%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓99.4%
(*.f64 (sqrt.f64 2) x)
Compiler

Compiled 10 to 8 computations (20% saved)

series1.0ms (0%)

Counts
1 → 0
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(*.f64 (sqrt.f64 2) x)
0.0ms
x
@inf
(*.f64 (sqrt.f64 2) x)
0.0ms
x
@-inf
(*.f64 (sqrt.f64 2) x)

rewrite57.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
1182×pow1
1084×add-exp-log
1084×log1p-expm1-u
1084×expm1-log1p-u
1058×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
113811
2150811
Stop Event
1×node limit
Counts
1 → 11
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) x)
Outputs
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(sqrt.f64 (*.f64 2 (*.f64 x x)))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))

simplify73.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
1896×log-prod
954×fma-neg
806×*-commutative
676×distribute-lft-out
640×distribute-rgt-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
032253
179187
2271121
31535121
44437121
56814121
Stop Event
1×node limit
Counts
11 → 14
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(sqrt.f64 (*.f64 2 (*.f64 x x)))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
Outputs
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(sqrt.f64 (*.f64 2 (*.f64 x x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)

eval3.0ms (0.1%)

Compiler

Compiled 92 to 77 computations (16.3% saved)

prune3.0ms (0.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New14014
Fresh000
Picked011
Done011
Total14216
Accurracy
100.0%
Counts
16 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(hypot.f64 x x)
✓99.4%
(*.f64 (sqrt.f64 2) x)
Compiler

Compiled 25 to 17 computations (32% saved)

regimes16.0ms (0.3%)

Accuracy

Total -30.1b remaining (-257014.7%)

Threshold costs -30.1b (-257014.7%)

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

4 calls:

7.0ms
x
3.0ms
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
3.0ms
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
3.0ms
(pow.f64 x 2)
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
100.0%1(+.f64 (pow.f64 x 2) (pow.f64 x 2))
100.0%1(pow.f64 x 2)
Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify4.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(hypot.f64 x x)
Outputs
(hypot.f64 x x)
Compiler

Compiled 4 to 2 computations (50% saved)

soundness267.0ms (5.3%)

Rules
2556×fma-def
1482×distribute-lft-out
1118×hypot-def
988×count-2
868×unswap-sqr
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0817
1147
2337
3567
41217
53807
613817
725897
839327
948607
1056267
1166377
1274947
Stop Event
1×node limit
Compiler

Compiled 28 to 15 computations (46.4% saved)

end0.0ms (0%)

preprocess19.0ms (0.4%)

Remove

(abs x)

Compiler

Compiled 34 to 22 computations (35.3% saved)

Profiling

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