Average Error: 32.2 → 0
Time: 989.0ms
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 r46489 = re;
        double r46490 = r46489 * r46489;
        double r46491 = im;
        double r46492 = r46491 * r46491;
        double r46493 = r46490 + r46492;
        double r46494 = sqrt(r46493);
        double r46495 = log(r46494);
        return r46495;
}
↓
double f(double re, double im) {
        double r46496 = 1.0;
        double r46497 = re;
        double r46498 = im;
        double r46499 = hypot(r46497, r46498);
        double r46500 = r46496 * r46499;
        double r46501 = log(r46500);
        return r46501;
}

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 32.2

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

  3. Applied *-un-lft-identity32.2

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

  4. Applied sqrt-prod32.2

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

  5. Simplified32.2

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

  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 2019354 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))