Average Error: 30.7 → 0.0
Time: 1.8s
Precision: 64
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\log \left(\mathsf{hypot}\left(re, im\right)\right)\]
\log \left(\sqrt{re \cdot re + im \cdot im}\right)
↓
\log \left(\mathsf{hypot}\left(re, im\right)\right)
double f(double re, double im) {
        double r875001 = re;
        double r875002 = r875001 * r875001;
        double r875003 = im;
        double r875004 = r875003 * r875003;
        double r875005 = r875002 + r875004;
        double r875006 = sqrt(r875005);
        double r875007 = log(r875006);
        return r875007;
}
↓
double f(double re, double im) {
        double r875008 = re;
        double r875009 = im;
        double r875010 = hypot(r875008, r875009);
        double r875011 = log(r875010);
        return r875011;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.7

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))