Average Error: 31.8 → 0
Time: 919.0ms
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 r48367 = re;
        double r48368 = r48367 * r48367;
        double r48369 = im;
        double r48370 = r48369 * r48369;
        double r48371 = r48368 + r48370;
        double r48372 = sqrt(r48371);
        double r48373 = log(r48372);
        return r48373;
}
↓
double f(double re, double im) {
        double r48374 = 1.0;
        double r48375 = sqrt(r48374);
        double r48376 = re;
        double r48377 = im;
        double r48378 = hypot(r48376, r48377);
        double r48379 = r48375 * r48378;
        double r48380 = log(r48379);
        return r48380;
}

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 31.8

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

  3. Applied *-un-lft-identity31.8

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

  4. Applied sqrt-prod31.8

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

  5. Simplified0

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

  6. Final simplification0

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))