Average Error: 31.3 → 0
Time: 1.1s
Precision: 64
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\log \left(1 \cdot \mathsf{hypot}\left(re, im\right)\right)\]
\log \left(\sqrt{re \cdot re + im \cdot im}\right)
↓
\log \left(1 \cdot \mathsf{hypot}\left(re, im\right)\right)
double f(double re, double im) {
        double r86097 = re;
        double r86098 = r86097 * r86097;
        double r86099 = im;
        double r86100 = r86099 * r86099;
        double r86101 = r86098 + r86100;
        double r86102 = sqrt(r86101);
        double r86103 = log(r86102);
        return r86103;
}
↓
double f(double re, double im) {
        double r86104 = 1.0;
        double r86105 = re;
        double r86106 = im;
        double r86107 = hypot(r86105, r86106);
        double r86108 = r86104 * r86107;
        double r86109 = log(r86108);
        return r86109;
}

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 31.3

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

  3. Applied *-un-lft-identity31.3

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

  4. Applied sqrt-prod31.3

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

  5. Simplified31.3

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

  6. Simplified0

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

  7. Final simplification0

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

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))