Average Error: 32.0 → 0.0
Time: 875.0ms
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 r35055 = re;
        double r35056 = r35055 * r35055;
        double r35057 = im;
        double r35058 = r35057 * r35057;
        double r35059 = r35056 + r35058;
        double r35060 = sqrt(r35059);
        double r35061 = log(r35060);
        return r35061;
}
↓
double f(double re, double im) {
        double r35062 = 1.0;
        double r35063 = sqrt(r35062);
        double r35064 = re;
        double r35065 = im;
        double r35066 = hypot(r35064, r35065);
        double r35067 = r35063 * r35066;
        double r35068 = log(r35067);
        return r35068;
}

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 2020025 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))