Average Error: 32.0 → 0.0
Time: 743.0ms
Precision: 64
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\log \left(\sqrt{1} \cdot \mathsf{hypot}\left(re, im\right)\right)\]
\log \left(\sqrt{re \cdot re + im \cdot im}\right)
↓
\log \left(\sqrt{1} \cdot \mathsf{hypot}\left(re, im\right)\right)
double f(double re, double im) {
        double r42850 = re;
        double r42851 = r42850 * r42850;
        double r42852 = im;
        double r42853 = r42852 * r42852;
        double r42854 = r42851 + r42853;
        double r42855 = sqrt(r42854);
        double r42856 = log(r42855);
        return r42856;
}
↓
double f(double re, double im) {
        double r42857 = 1.0;
        double r42858 = sqrt(r42857);
        double r42859 = re;
        double r42860 = im;
        double r42861 = hypot(r42859, r42860);
        double r42862 = r42858 * r42861;
        double r42863 = log(r42862);
        return r42863;
}

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 32.0

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
  2. Using strategy rm

  3. Applied *-un-lft-identity32.0

    \[\leadsto \log \left(\sqrt{\color{blue}{1 \cdot \left(re \cdot re + im \cdot im\right)}}\right)\]

  4. Applied sqrt-prod32.0

    \[\leadsto \log \color{blue}{\left(\sqrt{1} \cdot \sqrt{re \cdot re + im \cdot im}\right)}\]

  5. Simplified0.0

    \[\leadsto \log \left(\sqrt{1} \cdot \color{blue}{\mathsf{hypot}\left(re, im\right)}\right)\]

  6. Final simplification0.0

    \[\leadsto \log \left(\sqrt{1} \cdot \mathsf{hypot}\left(re, im\right)\right)\]

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))