?

Average Accuracy: 50.9% → 100.0%
Time: 1.6s
Precision: binary64
Cost: 12928

?

\[\log \left(\sqrt{re \cdot re + im \cdot im}\right) \]
↓
\[\log \left(\mathsf{hypot}\left(re, im\right)\right) \]
(FPCore (re im) :precision binary64 (log (sqrt (+ (* re re) (* im im)))))
↓
(FPCore (re im) :precision binary64 (log (hypot re im)))
double code(double re, double im) {
	return log(sqrt(((re * re) + (im * im))));
}
↓
double code(double re, double im) {
	return log(hypot(re, im));
}

public static double code(double re, double im) {
	return Math.log(Math.sqrt(((re * re) + (im * im))));
}
↓
public static double code(double re, double im) {
	return Math.log(Math.hypot(re, im));
}

def code(re, im):
	return math.log(math.sqrt(((re * re) + (im * im))))
↓
def code(re, im):
	return math.log(math.hypot(re, im))

function code(re, im)
	return log(sqrt(Float64(Float64(re * re) + Float64(im * im))))
end
↓
function code(re, im)
	return log(hypot(re, im))
end

function tmp = code(re, im)
	tmp = log(sqrt(((re * re) + (im * im))));
end
↓
function tmp = code(re, im)
	tmp = log(hypot(re, im));
end

code[re_, im_] := N[Log[N[Sqrt[N[(N[(re * re), $MachinePrecision] + N[(im * im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]
↓
code[re_, im_] := N[Log[N[Sqrt[re ^ 2 + im ^ 2], $MachinePrecision]], $MachinePrecision]

\log \left(\sqrt{re \cdot re + im \cdot im}\right)
↓
\log \left(\mathsf{hypot}\left(re, im\right)\right)

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 50.9%

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right) \]

  2. Simplified100.0%

    \[\leadsto \color{blue}{\log \left(\mathsf{hypot}\left(re, im\right)\right)} \]
    Proof

    [Start]50.9

    \[ \log \left(\sqrt{re \cdot re + im \cdot im}\right) \]

    hypot-def [=>]100.0

    \[ \log \color{blue}{\left(\mathsf{hypot}\left(re, im\right)\right)} \]

  3. Final simplification100.0%

    \[\leadsto \log \left(\mathsf{hypot}\left(re, im\right)\right) \]

Reproduce?

herbie shell --seed 2023126 
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))