Average Error: 32.3 → 0.6
Time: 3.1s
Precision: binary64
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10} \]
↓
\[\frac{-\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 0.1} \]
(FPCore (re im)
 :precision binary64
 (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)))
↓
(FPCore (re im) :precision binary64 (/ (- (log (hypot re im))) (log 0.1)))
double code(double re, double im) {
	return log(sqrt(((re * re) + (im * im)))) / log(10.0);
}
↓
double code(double re, double im) {
	return -log(hypot(re, im)) / log(0.1);
}

public static double code(double re, double im) {
	return Math.log(Math.sqrt(((re * re) + (im * im)))) / Math.log(10.0);
}
↓
public static double code(double re, double im) {
	return -Math.log(Math.hypot(re, im)) / Math.log(0.1);
}

def code(re, im):
	return math.log(math.sqrt(((re * re) + (im * im)))) / math.log(10.0)
↓
def code(re, im):
	return -math.log(math.hypot(re, im)) / math.log(0.1)

function code(re, im)
	return Float64(log(sqrt(Float64(Float64(re * re) + Float64(im * im)))) / log(10.0))
end
↓
function code(re, im)
	return Float64(Float64(-log(hypot(re, im))) / log(0.1))
end

function tmp = code(re, im)
	tmp = log(sqrt(((re * re) + (im * im)))) / log(10.0);
end
↓
function tmp = code(re, im)
	tmp = -log(hypot(re, im)) / log(0.1);
end

code[re_, im_] := N[(N[Log[N[Sqrt[N[(N[(re * re), $MachinePrecision] + N[(im * im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / N[Log[10.0], $MachinePrecision]), $MachinePrecision]
↓
code[re_, im_] := N[((-N[Log[N[Sqrt[re ^ 2 + im ^ 2], $MachinePrecision]], $MachinePrecision]) / N[Log[0.1], $MachinePrecision]), $MachinePrecision]

\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}
↓
\frac{-\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 0.1}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 32.3

    \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10} \]

  2. Simplified0.6

    \[\leadsto \color{blue}{\frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 10}} \]

  3. Applied egg-rr0.6

    \[\leadsto \color{blue}{-\frac{\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 0.1}} \]

  4. Final simplification0.6

    \[\leadsto \frac{-\log \left(\mathsf{hypot}\left(re, im\right)\right)}{\log 0.1} \]

Reproduce

herbie shell --seed 2022190 
(FPCore (re im)
  :name "math.log10 on complex, real part"
  :precision binary64
  (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)))