Average Error: 32.0 → 0.0
Time: 1.3s
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 r242 = re;
        double r243 = r242 * r242;
        double r244 = im;
        double r245 = r244 * r244;
        double r246 = r243 + r245;
        double r247 = sqrt(r246);
        double r248 = log(r247);
        return r248;
}
↓
double f(double re, double im) {
        double r249 = 1.0;
        double r250 = sqrt(r249);
        double r251 = re;
        double r252 = im;
        double r253 = hypot(r251, r252);
        double r254 = r250 * r253;
        double r255 = log(r254);
        return r255;
}

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)))))