math.log/1 on complex, real part

?

Percentage Accurate: 51.7% → 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)

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Herbie found 1 alternatives:

AlternativeAccuracySpeedup

Accuracy vs Speed

The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Bogosity?

Bogosity

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%

    \[\leadsto \color{blue}{\log \left(\mathsf{hypot}\left(re, im\right)\right)} \]
    Step-by-step derivation

    [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 2023178 
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))