Average Error: 32.4 → 0.0
Time: 521.0ms
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 r48001 = re;
        double r48002 = r48001 * r48001;
        double r48003 = im;
        double r48004 = r48003 * r48003;
        double r48005 = r48002 + r48004;
        double r48006 = sqrt(r48005);
        double r48007 = log(r48006);
        return r48007;
}
↓
double f(double re, double im) {
        double r48008 = re;
        double r48009 = im;
        double r48010 = hypot(r48008, r48009);
        double r48011 = log(r48010);
        return r48011;
}

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 32.4

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

  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 2020047 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))